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Abstract Background The proportion of nitrogen (N) derived from the atmosphere (Ndfa) is a fundamental component of the plant N demand in legume species. To estimate the N benefit of grain legumes for the subsequent crop in the rotation, a simplified N balance is frequently used. This balance is calculated as the difference between fixed N and removed N by grains. The Ndfa needed to achieve a neutral N balance (hereafter $$\theta$$ θ ) is usually estimated through a simple linear regression model between Ndfa and N balance. This quantity is routinely estimated without accounting for the uncertainty in the estimate, which is needed to perform formal statistical inference about $$\theta$$ θ . In this article, we utilized a global database to describe the development of a novel Bayesian framework to quantify the uncertainty of $$\theta$$ θ . This study aimed to (i) develop a Bayesian framework to quantify the uncertainty of $$\theta$$ θ , and (ii) contrast the use of this Bayesian framework with the widely used delta and bootstrapping methods under different data availability scenarios. Results The delta method, bootstrapping, and Bayesian inference provided nearly equivalent numerical values when the range of values for Ndfa was thoroughly explored during data collection (e.g., 6–91%), and the number of observations was relatively high (e.g., $$\ge 100$$ ≥ 100 ). When the Ndfa tested was narrow and/or sample size was small, the delta method and bootstrapping provided confidence intervals containing biologically non-meaningful values (i.e. 100%). However, under a narrow Ndfa range and small sample size, the developed Bayesian inference framework obtained biologically meaningful values in the uncertainty estimation. Conclusion In this study, we showed that the developed Bayesian framework was preferable under limited data conditions ─by using informative priors─ and when uncertainty estimation had to be constrained (regularized) to obtain meaningful inference. The presented Bayesian framework lays the foundation not only to conduct formal comparisons or hypothesis testing involving $$\theta$$ θ , but also to learn about its expected value, variance, and higher moments such as skewness and kurtosis under different agroecological and crop management conditions. This framework can also be transferred to estimate balances for other nutrients and/or field crops to gain knowledge on global crop nutrient balances.

Background: The proportion of nitrogen (N) derived from the atmosphere (Ndfa) is a fundamental component of the plant N demand in legume species. To estimate the N benefit of grain legumes for the subsequent crop in the rotation, a simplified N balance is frequently used. This balance is calculated as the difference between fixed N and removed N by grains. The Ndfa needed to achieve a neutral N balance (hereafter θ ) is usually estimated through a simple linear regression model between Ndfa and N balance. This quantity is routinely estimated without accounting for the uncertainty in the estimate, which is needed to perform formal statistical inference about θ . In this article, we utilized a global database to describe the development of a novel Bayesian framework to quantify the uncertainty of θ . This study aimed to (i) develop a Bayesian framework to quantify the uncertainty of θ , and (ii) contrast the use of this Bayesian framework with the widely used delta and bootstrapping methods under different data availability scenarios. Results: The delta method, bootstrapping, and Bayesian inference provided nearly equivalent numerical values when the range of values for Ndfa was thoroughly explored during data collection (e.g., 6–91%), and the number of observations was relatively high (e.g., ≥ 100 ). When the Ndfa tested was narrow and/or sample size was small, the delta method and bootstrapping provided confidence intervals containing biologically non-meaningful values (i.e. < 0% or > 100%). However, under a narrow Ndfa range and small sample size, the developed Bayesian inference framework obtained biologically meaningful values in the uncertainty estimation. Conclusion: In this study, we showed that the developed Bayesian framework was preferable under limited data conditions ─by using informative priors─ and when uncertainty estimation had to be constrained (regularized) to obtain meaningful inference. The presented Bayesian framework lays the foundation not only to conduct formal comparisons or hypothesis testing involving θ , but also to learn about its expected value, variance, and higher moments such as skewness and kurtosis under different agroecological and crop management conditions. This framework can also be transferred to estimate balances for other nutrients and/or field crops to gain knowledge on global crop nutrient balances. [ABSTRACT FROM AUTHOR]

In this paper, we used the maximum likelihood estimation (MLE) and the Bayes methods to perform estimation procedures for the reliability of stress-strength $ R = P(Y < X) $ based on independent adaptive progressive censored samples that were taken from the Chen distribution. An approximate confidence interval of $ R $ was constructed using a variety of classical techniques, such as the normal approximation of the MLE, the normal approximation of the log-transformed MLE, and the percentile bootstrap (Boot-p) procedure. Additionally, the asymptotic distribution theory and delta approach were used to generate the approximate confidence interval. Further, the Bayesian estimation of $ R $ was obtained based on the balanced loss function, which came in two versions here, the symmetric balanced squared error (BSE) loss function and the asymmetric balanced linear exponential (BLINEX) loss function. When estimating $ R $ using the Bayesian approach, all the unknown parameters of the Chen distribution were assumed to be independently distributed and to have informative gamma priors. Additionally, a mixture of Gibbs sampling algorithm and Metropolis-Hastings algorithm was used to compute the Bayes estimate of $ R $ and the associated highest posterior density credible interval. In the end, simulation research was used to assess the general overall performance of the proposed estimators and a real dataset was provided to exemplify the theoretical results.

In this paper, we used the maximum likelihood estimation (MLE) and the Bayes methods to perform estimation procedures for the reliability of stress-strength R = P(Y < X) based on independent adaptive progressive censored samples that were taken from the Chen distribution. An approximate confidence interval of R was constructed using a variety of classical techniques, such as the normal approximation of the MLE, the normal approximation of the log-transformed MLE, and the percentile bootstrap (Boot-p) procedure. Additionally, the asymptotic distribution theory and delta approach were used to generate the approximate confidence interval. Further, the Bayesian estimation of R was obtained based on the balanced loss function, which came in two versions here, the symmetric balanced squared error (BSE) loss function and the asymmetric balanced linear exponential (BLINEX) loss function. When estimating R using the Bayesian approach, all the unknown parameters of the Chen distribution were assumed to be independently distributed and to have informative gamma priors. Additionally, a mixture of Gibbs sampling algorithm and Metropolis-Hastings algorithm was used to compute the Bayes estimate of R and the associated highest posterior density credible interval. In the end, simulation research was used to assess the general overall performance of the proposed estimators and a real dataset was provided to exemplify the theoretical results. [ABSTRACT FROM AUTHOR]

This study investigates the asymptotic properties of method-of-moments estimators for the Birnbaum–Saunders distribution under a newly proposed parametrization. Theoretical derivations establish the asymptotic normality of these estimators, supported by explicit expressions for the mean vector and variance–covariance matrix. Simulation studies validate these results across various sample sizes and parameter values. A practical application is demonstrated through modeling cumulative rainfall data from northeastern Thailand, highlighting the distribution’s suitability for extreme weather prediction.

We used a class of stochastic differential equations (SDE) to model the evolution of cattle weight that, by an appropriate transformation of the weight, resulted in a variant of the Ornstein-Uhlenbeck model. In previous works, we have dealt with estimation, prediction, and optimization issues for this class of models. However, to incorporate individual characteristics of the animals, the average transformed size at maturity parameter α and/or the growth parameter β may vary randomly from animal to animal, which results in SDE mixed models. Obtaining a closed-form expression for the likelihood function to apply the maximum likelihood estimation method is a difficult, sometimes impossible, task. We compared the known Laplace approximation method with the delta method to approximate the integrals involved in the likelihood function. These approaches were adapted to allow the estimation of the parameters even when the requirement of most existing methods, namely having the same age vector of observations for all trajectories, fails, as it did in our real data example. Simulation studies were also performed to assess the performance of these approximation methods. The results show that the approximation methods under study are a very good alternative for the estimation of SDE mixed models. [ABSTRACT FROM AUTHOR]

We used a class of stochastic differential equations (SDE) to model the evolution of cattle weight that, by an appropriate transformation of the weight, resulted in a variant of the Ornstein-Uhlenbeck model. In previous works, we have dealt with estimation, prediction, and optimization issues for this class of models. However, to incorporate individual characteristics of the animals, the average transformed size at maturity parameter $ \alpha $ and/or the growth parameter $ \beta $ may vary randomly from animal to animal, which results in SDE mixed models. Obtaining a closed-form expression for the likelihood function to apply the maximum likelihood estimation method is a difficult, sometimes impossible, task. We compared the known Laplace approximation method with the delta method to approximate the integrals involved in the likelihood function. These approaches were adapted to allow the estimation of the parameters even when the requirement of most existing methods, namely having the same age vector of observations for all trajectories, fails, as it did in our real data example. Simulation studies were also performed to assess the performance of these approximation methods. The results show that the approximation methods under study are a very good alternative for the estimation of SDE mixed models.

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Sunlight plays a key role in the nutrient cycle within streams. Streams are often piped to accommodate urban residential or commercial development for buildings, roads, and parking. This results in altered exposure to sunlight, air, and soil, subsequently affecting the growth of aquatic vegetation, reducing reaeration, and thus impairing the water quality and ecological health of streams. While the effects of urbanization on urban streams, including changing flow regimes, stream bank and bed erosion, and degraded water quality, are well understood, the effects of piping streams on dissolved oxygen (DO) concentrations, fish habitats, reaeration, photosynthesis, and respiration rates are not. We addressed this research gap by assessing the effects of stream piping on DO concentrations before and after a 565-m piped section of Stroubles Creek in Blacksburg, VA, for several days during the summer of 2021. Results indicate that the DO level decreased by approximately 18.5% during daylight hours as water flowed through the piped section of the creek. Given the optimum DO level (9.0 mg·L−1) for brook trout (Salvelinus sp.), which are native and present in a portion of Stroubles Creek, the resulting DO deficits were − 0.49 and − 1.24 mg·L−1, for the inlet and outlet, respectively, indicating a possible adverse impact from piping the stream on trout habitat. Photosynthesis and respiration rates were reduced through the piped section, primarily due to the reduced solar radiation and the resultant reduction in oxygen production from aquatic vegetation; however, the reaeration rate increased. This study can inform watershed restoration efforts, particularly decisions regarding stream daylighting with respect to potential water quality and aquatic habitat benefits. [ABSTRACT FROM AUTHOR]

Abstract Background In integrative bioinformatic analyses, it is of great interest to stablish the equivalence between gene or (more in general) feature lists, up to a given level and in terms of their annotations in the Gene Ontology. The aim of this article is to present an equivalence test based on the proportion of GO terms which are declared as enriched in both lists simultaneously. Results On the basis of these data, the dissimilarity between gene lists is measured by means of the Sorensen–Dice index. We present two flavours of the same test: One of them based on the asymptotic normality of the test statistic and the other based on the bootstrap method. Conclusions The accuracy of these tests is studied by means of simulation and their possible interest is illustrated by using them over two real datasets: A collection of gene lists related to cancer and a collection of gene lists related to kidney rejection after transplantation.

Accurate estimation of the T-year return levels of climate extremes using statistical distribution is a critical step in the projection of future climate and in engineering design for disaster response. We show how the estimation of such quantities can be improved by fitting the four-parameter kappa distribution for r-largest order statistics (rK4D), which was developed in this study. The rK4D is an extension of the generalized extreme value distribution for r-largest order statistics (rGEVD), similar to the four-parameter kappa distribution (K4D), which is an extension of the generalized extreme value distribution (GEVD). This new distribution (rK4D) can be useful not only for fitting data when three parameters in the GEVD are not sufficient to capture the variability of the extreme observations, but also in reducing the estimation uncertainty by making use of the r-largest extreme observations instead of only the block maxima. We derive a joint probability density function (PDF) of rK4D and the marginal and conditional cumulative distribution functions and PDFs. To estimate the parameters, the maximum likelihood estimation and the maximum penalized likelihood estimation methods were considered. The usefulness and practical effectiveness of the rK4D are illustrated by the Monte Carlo simulation and by an application to the Bangkok extreme rainfall data. A few new distributions for r-largest order statistics are also derived as special cases of the rK4D, such as the r-largest logistic, the r-largest generalized logistic, and the r-largest generalized Gumbel distributions. These distributions for r-largest order statistics would be useful in modeling extreme values for many research areas, including hydrology and climatology.

Over the past decade, a series of procedures has been introduced to estimate, using a non-iterative method, the linear-by-linear association parameter of an ordinal log-linear model. This paper will examine the two key non-iteratively determined estimates of the parameter for the analysis of the association between the two categorical variables that form a contingency table; these are the log and the Beh-Davy non-iterative estimates, referred to simply as the LogNI and the BDNI estimates, respectively. Such an examination will focus on determining their asymptotic characteristics. To do so, a computational study was undertaken for tables of varying sizes to show that these two estimates are asymptotically unbiased. It is also shown that both estimates are asymptotically normally distributed. On the basis of the standard errors, their relative efficiency was established for the 13 commonly analysed contingency tables that appear throughout the literature. [ABSTRACT FROM AUTHOR]

This study uses the adaptive Type-II progressively censored competing risks model to estimate the unknown parameters and the survival function of the Gompertz distribution. Where the lifetime for each failure is considered independent, and each follows a unique Gompertz distribution with different shape parameters. First, the Newton-Raphson method is used to derive the maximum likelihood estimators (MLEs), and the existence and uniqueness of the estimators are also demonstrated. We used the stochastic expectation maximization (SEM) method to construct MLEs for unknown parameters, which simplified and facilitated computation. Based on the asymptotic normality of the MLEs and SEM methods, we create the corresponding confidence intervals for unknown parameters, and the delta approach is utilized to obtain the interval estimation of the reliability function. Additionally, using two bootstrap techniques, the approximative interval estimators for all unknowns are created. Furthermore, we computed the Bayes estimates of unknown parameters as well as the survival function using the Markov chain Monte Carlo (MCMC) method in the presence of square error and LINEX loss functions. Finally, we look into two real data sets and create a simulation study to evaluate the efficacy of the established approaches. [ABSTRACT FROM AUTHOR]

Abstract Background Loss to follow-up is a major challenge for very preterm (VPT) cohorts; attrition is associated with social disadvantage and parents with impaired children may participate less in research. We investigated the impact of loss to follow-up on the estimated prevalence of neurodevelopmental impairment in a VPT cohort using different methodological approaches. Methods This study includes births

Molecular weight distributions are widely used to evaluate the effects of aging or modifiers in bituminous binders. As with polymers, the most common techniques to obtain the distributions can be subdivided into two main groups, depending on whether or not they use a solvent. In the first group, the dimension of the molecules is evaluated in a diluted unperturbed state, while, in the second, the dimension derives from the bulk, where aggregated or interacting molecules may behave as single entities. However, the calibration curves used in the bulk are tuned in order to homogenize the results derived from the two approaches. This sort of contradiction, plus the high number of experimental uncertainties, suggest that the term "apparent" should be used for both distributions. These aspects are well known in the field of polymers but have received less attention in the case of bitumens, which are even more complex. This paper pinpoints the advantages and disadvantages of the two techniques, thus highlighting the most appropriate use. Bulk methods are preferred when evaluating properties that are strictly dependent on the microstructure, such as the level of aging and the effects of additives or modifiers. Diluted methods should be used when the molecular size matters, such as in quantifying the presence of polymers or rejuvenators. Both techniques should be used for comparative studies only. [ABSTRACT FROM AUTHOR]

In many environmental and ecological settings, the analysis of data involves calculation of a confidence interval for a nonlinear function of the model parameters. In the frequentist approach, this is often achieved by using a Wald interval in which the standard error of the estimate of the function is obtained using the delta method.The purpose of this paper is to promote a simple alternative to the delta method that will provide better coverage properties when the estimates of the model parameters have a distribution that is approximately multivariate normal, as will be the case asymptotically for maximum likelihood estimates in regular models. We propose a simple diagnostic tool that can be used to assess the reliability of this assumption.The method we promote can be thought of as a computationally efficient version of parametric bootstrapping, as it mimics such bootstrapping without a need to refit the model.We provide two examples to illustrate use of the new method and present simulation results which show that its coverage properties are superior to those for a Wald interval based on the delta method when the assumption of normality for the estimates of the model parameters is reliable. We also compare its coverage properties and computational effort with those of parametric bootstrapping. [ABSTRACT FROM AUTHOR]

Abstract Background A new variance estimator is derived and tested for big BAF (Basal Area Factor) sampling which is a forest inventory system that utilizes Bitterlich sampling (point sampling) with two BAF sizes, a small BAF for tree counts and a larger BAF on which tree measurements are made usually including DBHs and heights needed for volume estimation. Methods The new estimator is derived using the Delta method from an existing formulation of the big BAF estimator as consisting of three sample means. The new formula is compared to existing big BAF estimators including a popular estimator based on Bruce’s formula. Results Several computer simulation studies were conducted comparing the new variance estimator to all known variance estimators for big BAF currently in the forest inventory literature. In simulations the new estimator performed well and comparably to existing variance formulas. Conclusions A possible advantage of the new estimator is that it does not require the assumption of negligible correlation between basal area counts on the small BAF factor and volume-basal area ratios based on the large BAF factor selection trees, an assumption required by all previous big BAF variance estimation formulas. Although this correlation was negligible on the simulation stands used in this study, it is conceivable that the correlation could be significant in some forest types, such as those in which the DBH-height relationship can be affected substantially by density perhaps through competition. We derived a formula that can be used to estimate the covariance between estimates of mean basal area and the ratio of estimates of mean volume and mean basal area. We also mathematically derived expressions for bias in the big BAF estimator that can be used to show the bias approaches zero in large samples on the order of 1 n $\frac {1}{n}$ where n is the number of sample points.

Background: In integrative bioinformatic analyses, it is of great interest to stablish the equivalence between gene or (more in general) feature lists, up to a given level and in terms of their annotations in the Gene Ontology. The aim of this article is to present an equivalence test based on the proportion of GO terms which are declared as enriched in both lists simultaneously. Results: On the basis of these data, the dissimilarity between gene lists is measured by means of the Sorensen–Dice index. We present two flavours of the same test: One of them based on the asymptotic normality of the test statistic and the other based on the bootstrap method. Conclusions: The accuracy of these tests is studied by means of simulation and their possible interest is illustrated by using them over two real datasets: A collection of gene lists related to cancer and a collection of gene lists related to kidney rejection after transplantation. [ABSTRACT FROM AUTHOR]

The predicted climate change threatens food security in the coming years in Algeria. So, this study aims to assess the impact of future climate change on a key crop in Algeria which is rainfed durum wheat. We investigate the impact of climate change on rainfed durum wheat cultivar called Mexicali using AquaCrop crop model and the EURO-CORDEX climate projections downscaled with the ICHEC_KNMI model under RCP 4.5 and RCP 8.5. A delta method was applied to correct the incertitudes present in the raw climate projections of two experimental sites located in Sétif and Bordj Bou Arreridj (BBA)'s Eastern High plains of Algeria (EHPs). AquaCrop was validated with a good precision (RMSE = 0.41 tha−1) to simulate Mexicali cultivar yields. In 2035–2064, it is expected at both sites: an average wheat grain yield enhances of +49% and +105% under RCP 4.5 and RCP 8.5, respectively, compared to the average yield of the baseline period (1981–2010), estimated at 29 qha−1. In both sites, in 2035–2064, under RCP 4.5 and RCP 8.5, the CO2 concentrations elevation has a fertilizing effect on rainfed wheat yield. This effect compensates for the negative impacts induced by the temperatures increase and decline in precipitation and net solar radiation. An increase in wheat water productivity is predicted under both RCPs scenarios. That is due to the water loss drop induced by the shortening of the wheat-growing cycle length by the effect of temperatures increase. In 2035–2064, early sowing in mid-September and October will lead to wheat yields improvement, as it will allow the wheat plant to benefit from the precipitations increase through the fall season. Thus, this early sowing will ensure a well vegetative development and will allow the wheat's flowering and grain filling before the spring warming period. [ABSTRACT FROM AUTHOR]

Abstract Background The double sampling method known as “big BAF sampling” has been advocated as a way to reduce sampling effort while still maintaining a reasonably precise estimate of volume. A well-known method for variance determination, Bruce’s method, is customarily used because the volume estimator takes the form of a product of random variables. However, the genesis of Bruce’s method is not known to most foresters who use the method in practice. Methods We establish that the Taylor series approximation known as the Delta method provides a plausible explanation for the origins of Bruce’s method. Simulations were conducted on two different tree populations to ascertain the similarities of the Delta method to the exact variance of a product. Additionally, two alternative estimators for the variance of individual tree volume-basal area ratios, which are part of the estimation process, were compared within the overall variance estimation procedure. Results The simulation results demonstrate that Bruce’s method provides a robust method for estimating the variance of inventories conducted with the big BAF method. The simulations also demonstrate that the variance of the mean volume-basal area ratios can be computed using either the usual sample variance of the mean or the ratio variance estimators with equal accuracy, which had not been shown previously for Big BAF sampling. Conclusions A plausible explanation for the origins of Bruce’s method has been set forth both historically and mathematically in the Delta Method. In most settings, there is evidently no practical difference between applying the exact variance of a product or the Delta method—either can be used. A caution is articulated concerning the aggregation of tree-wise attributes into point-wise summaries in order to test the correlation between the two as a possible indicator of the need for further covariance augmentation.

Abstract The interpretation of odds ratios (OR) as prevalence ratios (PR) in cross-sectional studies have been criticized since this equivalence is not true unless under specific circumstances. The logistic regression model is a very well known statistical tool for analysis of binary outcomes and frequently used to obtain adjusted OR. Here, we introduce the prLogistic for the R statistical computing environment which can be obtained from The Comprehensive R Archive Network, https://cran.r-project.org/package=prLogistic. The package prLogistic was built to assist the estimation of PR via logistic regression models adjusted by delta method and bootstrap for analysis of independent and correlated binary data. Two applications are presented to illustrate its use for analysis of independent observations and data from clustered studies.

In Australia, trifluralin is one of the commonly used herbicides to manage annual grasses and some broadleaf weeds. However, it may have some ecosystem impacts such as high toxicity to terrestrial and aquatic life, so it is vital to monitor the degradation of trifluralin for a considerable period for environmental safety. For risk assessment purposes, it is necessary to estimate the half-life of trifluralin, which is often evaluated using derived mathematical dissipation models. In the literature, bi-exponential (BEXP) and gamma models were suggested for modelling the dissipation of trifluralin in soil. Both models provide the half-life estimate without discussing the uncertainty of the estimate, which is a shortcoming in the literature. In this paper, we used simulation to illustrate the importance of estimate's uncertainty (standard error) and demonstrated a method to compute the standard error for the half-life estimate mathematically for kinetic dissipation models. Later, we evaluated the performance of the two suggested models using statistical indices. The computation of the half-life and the standard error of the half-life estimate were discussed. This allows us to describe the inference of the half-life parameter and determine whether the half-life estimates are significantly different against the co-variate (moisture) levels. We demonstrated the method to calculate the standard error of the half-life of trifluralin, which allows us to determine the statistical difference between the estimates. In this study, we found that the half-life of trifluralin in soil tends to increase with increasing moisture levels, and the half-life of trifluralin in soil with 100% moisture level is significantly greater than 40% and 70% moisture levels. Our findings suggest that soil moisture levels should be carefully considered before trifluralin application to minimize the non-target environmental damage. [Display omitted] • BEXP and gamma models have been considered to investigate the trifluralin dissipation. • A simulation study illustrated the importance of the standard error of half-life. • Provided mathematical computation of the standard error of the half-life. • The soil moisture levels influenced the half-life estimates of trifluralin. [ABSTRACT FROM AUTHOR]

In reliability and life testing experiments, obtaining complete data still consumes lots of time, financial and human supports. A censoring scheme which can have balance between the total testing time, the used number of units and cost in life tests is desirable. Nevertheless, with short product development times, life testing experiments must be performed with severe time constraints, which makes failure-censored schemes such as type-II censoring and progressive type-II censoring schemes are no longer applicable in many real life scenarios. Therefore, an adaptive type-I progressive hybrid censoring scheme has been shown to be useful in this case, which assures the termination of the life testing experiment at a predetermined time and results in a higher efficiency estimations. In this paper we consider the estimation problem of parameters, reliability and hazard rate functions of a two-parameter bathtub-shaped distribution under adaptive type-I progressive hybrid censoring scheme using the maximum likelihood and Bayesian estimation methods. Lindley's approximation and an importance sampling procedure under the assumption of independent gamma priors are used to obtain the Bayes estimators. Approximate confidence, two parametric bootstrap and highest posterior density intervals are also obtained for the unknown parameters, reliability and hazard rate functions. The approximate confidence intervals of the reliability and hazard rate functions are obtained by estimating their variances using delta method. A simulation study is conducted to compare the performance of the different estimators in terms of their mean squared errors and interval lengths. Finally, two real data sets are analyzed to show the applicability of the different estimations. The data analysis showed that the adaptive type-I progressive hybrid censoring scheme is flexible and very useful in terminating the experiment when the time is the main concern to the experimenter.

Over the past decade, a series of procedures has been introduced to estimate, using a non-iterative method, the linear-by-linear association parameter of an ordinal log-linear model. This paper will examine the two key non-iteratively determined estimates of the parameter for the analysis of the association between the two categorical variables that form a contingency table; these are the log and the Beh-Davy non-iterative estimates, referred to simply as the LogNI and the BDNI estimates, respectively. Such an examination will focus on determining their asymptotic characteristics. To do so, a computational study was undertaken for tables of varying sizes to show that these two estimates are asymptotically unbiased. It is also shown that both estimates are asymptotically normally distributed. On the basis of the standard errors, their relative efficiency was established for the 13 commonly analysed contingency tables that appear throughout the literature.

In this study, the delta method was applied to estimate the standard errors of the true score equating when using the characteristic curve methods with the generalized partial credit model in test equating under the context of the common-item nonequivalent groups equating design. Simulation studies were further conducted to compare the performance of the delta method with that of the bootstrap method and the multiple imputation method. The results indicated that the standard errors produced by the delta method were very close to the criterion empirical standard errors as well as those yielded by the bootstrap method and the multiple imputation method under all the manipulated conditions. [ABSTRACT FROM AUTHOR]

Background: Loss to follow-up is a major challenge for very preterm (VPT) cohorts; attrition is associated with social disadvantage and parents with impaired children may participate less in research. We investigated the impact of loss to follow-up on the estimated prevalence of neurodevelopmental impairment in a VPT cohort using different methodological approaches.Methods: This study includes births < 32 weeks of gestational age (GA) from 4 regions in the UK and Portugal participating in a European birth cohort (N = 1737 survivors). Data on maternal characteristics, pregnancy complications, neonatal outcomes and neighborhood deprivation were collected at baseline. Neurodevelopment was assessed at 2 years of corrected age (CA) using standardized parent-report measures. We applied (1) multiple imputation (MI) and (2) inverse probability weighting (IPW) to estimate the impact of non-response on the prevalence of moderate to severe neurodevelopmental impairment and assessed violations of the missing at random (MAR) assumption using the delta method.Results: 54.2% of children were followed-up. Follow-up was less likely when mothers were younger, multiparous, foreign-born, did not breastfeed and came from deprived areas. The prevalence of neurodevelopmental impairment was 18.4% (95% confidence interval (CI):15.9-21.1) and increased to 20.4% (95%CI: 17.3-23.4) and 20.0% (95%CI:16.9-23.1) for MI and IPW models, respectively. Simulating strong violations of MAR (children with impairments being 50% less likely to be followed-up) raised estimates to 23.6 (95%CI:20.1-27.1) CONCLUSIONS: In a VPT cohort with high loss to follow-up, correcting for attrition yielded modest increased estimates of neurodevelopmental impairment at 2 years CA; estimates were relatively robust to violations of the MAR assumption. [ABSTRACT FROM AUTHOR]

Background: A new variance estimator is derived and tested for big BAF (Basal Area Factor) sampling which is a forest inventory system that utilizes Bitterlich sampling (point sampling) with two BAF sizes, a small BAF for tree counts and a larger BAF on which tree measurements are made usually including DBHs and heights needed for volume estimation. Methods: The new estimator is derived using the Delta method from an existing formulation of the big BAF estimator as consisting of three sample means. The new formula is compared to existing big BAF estimators including a popular estimator based on Bruce's formula. Results: Several computer simulation studies were conducted comparing the new variance estimator to all known variance estimators for big BAF currently in the forest inventory literature. In simulations the new estimator performed well and comparably to existing variance formulas. Conclusions: A possible advantage of the new estimator is that it does not require the assumption of negligible correlation between basal area counts on the small BAF factor and volume-basal area ratios based on the large BAF factor selection trees, an assumption required by all previous big BAF variance estimation formulas. Although this correlation was negligible on the simulation stands used in this study, it is conceivable that the correlation could be significant in some forest types, such as those in which the DBH-height relationship can be affected substantially by density perhaps through competition. We derived a formula that can be used to estimate the covariance between estimates of mean basal area and the ratio of estimates of mean volume and mean basal area. We also mathematically derived expressions for bias in the big BAF estimator that can be used to show the bias approaches zero in large samples on the order of 1 n where n is the number of sample points. [ABSTRACT FROM AUTHOR]

Researchers have developed a characteristic curve procedure to estimate the parameter scale transformation coefficients in test equating under the nominal response model. In the study, the delta method was applied to derive the standard error expressions for computing the standard errors for the estimates of the parameter scale transformation coefficients. This brief report presents the results of a simulation study that examined the accuracy of the derived formulas and compared the performance of this analytical method with that of the multiple imputation method. The results indicated that the standard errors produced by the delta method were very close to the criterion standard errors as well as those yielded by the multiple imputation method under all the simulation conditions. [ABSTRACT FROM AUTHOR]

Background: The double sampling method known as "big BAF sampling" has been advocated as a way to reduce sampling effort while still maintaining a reasonably precise estimate of volume. A well-known method for variance determination, Bruce's method, is customarily used because the volume estimator takes the form of a product of random variables. However, the genesis of Bruce's method is not known to most foresters who use the method in practice. Methods: We establish that the Taylor series approximation known as the Delta method provides a plausible explanation for the origins of Bruce's method. Simulations were conducted on two different tree populations to ascertain the similarities of the Delta method to the exact variance of a product. Additionally, two alternative estimators for the variance of individual tree volume-basal area ratios, which are part of the estimation process, were compared within the overall variance estimation procedure. Results: The simulation results demonstrate that Bruce's method provides a robust method for estimating the variance of inventories conducted with the big BAF method. The simulations also demonstrate that the variance of the mean volume-basal area ratios can be computed using either the usual sample variance of the mean or the ratio variance estimators with equal accuracy, which had not been shown previously for Big BAF sampling. Conclusions: A plausible explanation for the origins of Bruce's method has been set forth both historically and mathematically in the Delta Method. In most settings, there is evidently no practical difference between applying the exact variance of a product or the Delta method—either can be used. A caution is articulated concerning the aggregation of tree-wise attributes into point-wise summaries in order to test the correlation between the two as a possible indicator of the need for further covariance augmentation. [ABSTRACT FROM AUTHOR]

Several sources of bias are involved at each stage of a quantitative precipitation estimation process because weather radars measure precipitation amounts indirectly. Conventional methods compare the relative uncertainties between different stages of the process but seldom present the total uncertainty. Therefore, the objectives of this study were as follows: (1) to quantify the uncertainty at each stage of the process and in total; (2) to elucidate the ratio of the uncertainty at each stage in terms of the total uncertainty; and (3) to explain the uncertainty propagation process at each stage. This study proposed novel application of three methods (maximum entropy method, uncertainty Delta method, and modified-fractional uncertainty method) to determine the total uncertainty, level of uncertainty increase, and percentage of uncertainty at each stage. Based on data from 18 precipitation events that occurred over the Korean Peninsula, the applicability of the three methods was tested using a radar precipitation estimation process that comprised two quality control algorithms, two precipitation estimation methods, and two post-processing precipitation bias correction methods. Results indicated that the final uncertainty of each method was reduced in comparison with the initial uncertainty, and that the uncertainty was different at each stage depending on the method applied. [ABSTRACT FROM AUTHOR]

Two-level Mokken scale analysis is a generalization of Mokken scale analysis for multi-rater data. The bias of estimated scalability coefficients for two-level Mokken scale analysis, the bias of their estimated standard errors, and the coverage of the confidence intervals has been investigated, under various testing conditions. It was found that the estimated scalability coefficients were unbiased in all tested conditions. For estimating standard errors, the delta method and the cluster bootstrap were compared. The cluster bootstrap structurally underestimated the standard errors of the scalability coefficients, with low coverage values. Except for unequal numbers of raters across subjects and small sets of items, the delta method standard error estimates had negligible bias and good coverage. Post hoc simulations showed that the cluster bootstrap does not correctly reproduce the sampling distribution of the scalability coefficients, and an adapted procedure was suggested. In addition, the delta method standard errors can be slightly improved if the harmonic mean is used for unequal numbers of raters per subject rather than the arithmetic mean. [ABSTRACT FROM AUTHOR]

We use a simple delta method to prove the Weyl bound in t -aspect for the L -function of a holomorphic or a Hecke-Maass cusp form of arbitrary level and nebentypus. In particular, this extends the results of Meurman and Jutila for the t -aspect Weyl bound, and the recent result of Booker, Milinovich and Ng to Hecke cusp forms of arbitrary level and nebentypus. [ABSTRACT FROM AUTHOR]

Faced with the lack of reliability and reproducibility in omics studies, more careful and robust methods are needed to overcome the existing challenges in the multi-omics analysis. In conventional omics data analysis, signal intensity values (denoted by M and values) are estimated neglecting pixel-level uncertainties, which may reflect noise and systematic artifacts. For example, intensity values from two-color microarray data are estimated by taking the mean or median of the pixel intensities within the spot and then subjected to a within-slide normalization by LOWESS. Thus, focusing on estimation and normalization of gene expression profiles, we propose a spot quantification method that takes into account pixel-level variability. Also, to preserve relevant variation that may be removed in LOWESS normalization with poorly chosen parameters, we propose a parameter selection method that is parsimonious and considers intrinsic characteristics of microarray data, such as heteroskedasticity. The usefulness of the proposed methods is illustrated by an application to real intestinal metaplasia data. Compared with the conventional approaches, the analysis is more robust and conservative, identifying fewer but more reliable differentially expressed genes. Also, the variability preservation allowed the identification of new differentially expressed genes. Using the proposed approach, we have identified differentially expressed genes involved in pathways in cancer and confirmed some molecular markers already reported in the literature.

In this paper some resampling methods for the extrema of certain conditional functions, including delta method along with jackknifing and bootstrapping, are examined, and the properties of the resulted statistics are discussed.

Building on prior research on the relationships between key concepts in item response theory and classical test theory, this note contributes to highlighting their important and useful links. A readily and widely applicable latent variable modeling procedure is discussed that can be used for point and interval estimation of the individual person true score on any item in a unidimensional multicomponent measuring instrument or item set under consideration. The method adds to the body of research on the connections between classical test theory and item response theory. The outlined estimation approach is illustrated on empirical data. [ABSTRACT FROM AUTHOR]

The problem of estimating the parameters m and p of the binomial distribution for a sample having the fixed volume n with the help of the method of moments is considered in this paper. Using the delta method, the joint asymptotic normality of the estimates is established and the parameters of the limit distribution are calculated. The moment estimates of the parameters m and p do not have averages and variance. An explanation is offered for the asymptotic normality parameters in terms of characteristics of the accuracy properties of the estimates. On the basis of the data of statistical modelling, the accuracy properties of the estimates by the delta-method and their modifications which do not have initial defects of the estimates (the values of the estimates of p are below zero and those of m are smaller than the greatest value in the sample) are explored. An example of estimating the parameters m and p according to the observations of the number of responses in the experiment with nervous synapse (m is the number of vesicles with acetylcholine in the vicinity of the synapse, p is the probability of acetylcholine release by each vesicle) is provided.

Several sources of bias are involved at each stage of a quantitative precipitation estimation process because weather radars measure precipitation amounts indirectly. Conventional methods compare the relative uncertainties between different stages of the process but seldom present the total uncertainty. Therefore, the objectives of this study were as follows: (1) to quantify the uncertainty at each stage of the process and in total; (2) to elucidate the ratio of the uncertainty at each stage in terms of the total uncertainty; and (3) to explain the uncertainty propagation process at each stage. This study proposed novel application of three methods (maximum entropy method, uncertainty Delta method, and modified-fractional uncertainty method) to determine the total uncertainty, level of uncertainty increase, and percentage of uncertainty at each stage. Based on data from 18 precipitation events that occurred over the Korean Peninsula, the applicability of the three methods was tested using a radar precipitation estimation process that comprised two quality control algorithms, two precipitation estimation methods, and two post-processing precipitation bias correction methods. Results indicated that the final uncertainty of each method was reduced in comparison with the initial uncertainty, and that the uncertainty was different at each stage depending on the method applied.

In this paper, the reliability of a k-component system, in which all components are subject to common stress, is considered. The multicomponent system will continue to survive if at least s out of k components’ strength exceed the common stress. The system reliability is investigated by utilizing the maximum likelihood estimator based on progressively type II censored samples from generalized Pareto distributions. The confidence interval of the system reliability can be obtained by using asymptotic normality with Fisher information matrix or bootstrap method approximation. An intensive simulation study is conducted to evaluate the performance of maximum likelihood estimators of the model parameters and system reliability for a variety of cases. For the confidence interval of the system reliability, simulation results indicate the bootstrap method approximation outperforms over the asymptotic normality approximation in terms of coverage probability.

Raindrop size distributions have been characterized through the gamma family. Over the years, quite a few estimates of these gamma parameters have been proposed. The natural question for the practitioner, then, is what estimation procedure should be used. We provide guidance in answering this question when a large sample size (>2000 drops) of accurately measured drops is available. Seven estimation procedures from the literature: five method of moments procedures, maximum likelihood, and a pseudo maximum likelihood procedure, were examined. We show that the two maximum likelihood procedures provide the best precision (lowest variance) in estimating the gamma parameters. Method of moments procedures involving higher-order moments, on the other hand, give rise to poor precision (high variance) in estimating these parameters. A technique called the delta method assisted in our comparison of these various estimation procedures.

Health disparities are differences in health status across different socioeconomic groups. Classical methods, e.g., the Delta method, have been used to estimate the standard errors of estimated measures of health disparities and to construct confidence intervals for these measures. However, the confidence intervals constructed using the classical methods do not have good coverage properties for situations involving sparse data. In this article, we introduce three new methods to construct fiducial intervals for measures of health disparities based on approximate fiducial quantities. Through a comprehensive simulation study, We compare the empirical coverage properties of the proposed fiducial intervals against two Monte Carlo simulation-based methods-utilizing either a truncated Normal distribution or the Gamma distribution-as well as the classical method. The findings of the simulation study advocate for the adoption of the Monte Carlo simulation-based method with the Gamma distribution when a unified approach is sought for all health disparity measures.

Study Region: The Wami River sub-basin is among the river sub-basins with a vital ecosystem in Tanzania. It comprises the Saadani National park and it has the very great potential of irrigation and rain fed agriculture. Study Focus: The objective of this study was to evaluate the uncertainty of future streamflow in respect of increasing water demands and uncertain projected climate inputs, General Circulation Models (GCMs). The water demands were projected to the year 2039 and GCM precipitation was selected as the changing climatic variable. The CMIP5-GCMs were evaluated for their skills and those with the minimum skill scores above 75% were downscaled and used in projection of scenario RCP 8.5 precipitation. Then uncertainties of RCP 8.5 precipitation were estimated using a fuzzy extension principle and finally used to simulate uncertainties of future runoff using a rainfall-runoff model, Soil and Water Assessment Tool (SWAT). New Hydrological Insights for the Region: The results of projected streamflow shows that the baseline annual climatology flow (ACF) is 98 m3/s and for the future, the median ACF is projected to be 81 m3/s. At 100% uncertainty of skilled projections, the ACF from the sub-basin is projected to range between −47% and +36% from the baseline ACF. However, the midstream of the sub-basin shows reliable water availability for foreseen water uses expansion up to the year 2039.

Stress-strength reliability problems arise frequently in applied statistics and related fields. Often they involve two independent and possibly small samples of measurements on strength and breakdown pressures (stress). The goal of the researcher is to use the measurements to obtain inference on reliability, which is the probability that stress will exceed strength. This paper addresses the case where reliability is expressed in terms of an integral which has no closed form solution and where the number of observed values on stress and strength is small. We find that the Lagrange approach to estimating constrained likelihood, necessary for inference, often performs poorly. We introduce a penalized likelihood method and it appears to always work well. We use third order likelihood methods to partially offset the issue of small samples. The proposed method is applied to draw inferences on reliability in stress-strength problems with independent exponentiated exponential distributions. Simulation studies are carried out to assess the accuracy of the proposed method and to compare it with some standard asymptotic methods.