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In this article, we have proposed a new confidence interval for the product of standardized generalized variance for k-multivariate normal populations. The results are reported in terms of coverage...

It is quite appealing to extend existing theories in classical linear models to correlated responses where linear mixed-effects models are utilized and the dependency in the data is modeled by random effects. In the mixed modeling framework, missing values occur naturally due to dropouts or non-responses, which is frequently encountered when dealing with real data. Motivated by such problems, we aim to investigate the estimation and model selection performance in linear mixed models when missing data are present. Inspired by the property of the indicator function for missingness and its relation to missing rates, we propose an approach that records missingness in an indicator-based matrix and derive the likelihood-based estimators for all parameters involved in the linear mixed-effects models. Based on the proposed method for estimation, we explore the relationship between estimation and selection behavior over missing rates. Simulations and a real data application are conducted for illustrating the effectiveness of the proposed method in selecting the most appropriate model and in estimating parameters.

In this article, we propose new confidence intervals for the population mean and variance, the ratio of two populations variance, and the difference in the arithmetic averages of two populations wi...

Evaluation of hospital quality is of great significance for the promotion of the development of medical care. Hospital standardized mortality ratio (HSMR) is the ratio of hospital observed mortalit...

Based on a progressively type-II censored sample from the exponential distribution with unknown location and scale parameter, confidence bands are proposed for the underlying distribution function by using confidence regions for the parameters and Kolmogorov-Smirnov type statistics. Simple explicit representations for the boundaries and for the coverage probabilities of the confidence bands are analytically derived, and the performance of the bands is compared in terms of band width and area by means of a data example. As a by-product, a novel confidence region for the location-scale parameter is obtained. Extensions of the results to related models for ordered data, such as sequential order statistics, as well as to other underlying location-scale families of distributions are discussed., AOM. This article has been accepted for publication in Journal of Statistical Computation and Simulation, published by Taylor & Francis

Several methods of finding interval estimators of the parameters of the gamma distribution are considered in the literature. In this work we compare the following methods: Wald confidence intervals...

The proportion of conformance is defined as the proportion of products with quality characteristic inside the specification limits. The construction of confidence interval for the proportion of con...

Capture-recapture is a popular sampling method to estimate the total number of individuals in a population. This method is also used to estimate the size of a target population based on several inc...

The problems of constructing confidence intervals (CIs) for the proportions and functions of proportions in finite populations are considered. For estimating the proportion in a finite population, ...

We consider the confidence interval for the univariate linear calibration, where a response variable is related to an explanatory variable by a simple linear model, and the observations of the resp...

The zero-inflated Poisson (ZIP) model is often postulated for count data that include excessive zeros. This ZIP distribution can be regarded as the mixture of two distributions, one that degenerate...

Frequentist and Bayesian approaches for interval estimation usually produce conflicting results if applied to analyze the same data set. Paradoxically, there is no unanimity in the literature on wh...

We study interval estimation for both parameters of the hypergeometric distribution: (i) the number of successes in a finite population and (ii) the size of the population. In contrast to tradition...

The Gini index has been widely used as a measure of income (or wealth) inequality in social sciences. To construct a confidence interval for the difference of two Gini indices from the pair...

The Asian economic crises of 1997 and the 2008 Global Financial Crisis (GFC) had far-reaching impacts on Asian and other global economies. Turmoil in the banking and finance sectors led to downturns in stock markets, resulting in bankruptcies, house repossessions and high unemployment. These crises have been shown to be correlated with a deterioration in mental health and an increase in suicides, and it is important to understand the implication of these impacts and how such recessions affect the health of affected populations. With the benefit of hindsight, did lessons learned from the negative effects of the 1997 Asian economic recession impact the aftermath of the 2008 GFC in Asian countries? Utilising a framework based on a simple strata-bootstrap algorithm using daily data – where available – we investigate the trend in suicide rates over time in three different populations (Hong Kong, Taiwan and South Korea), and examine whether there were any changes in the pattern of suicide rates in each country subsequent to both the 1997 Asian and 2008. We find that each country responded differently to each of the crises and the suicide rates for certain age-gender specific groups in each country were more affected.

Recent research has shown that interval estimators with good coverage properties are achievable for some functions of quantiles, even when sample sizes are not large. Motivated by this, we consider interval estimators for the ratios of independent quantiles and interquantile ranges that will be useful when comparing location and scale for two samples. Simulations show that the intervals have excellent coverage properties for a wide range of distributions, including those that are heavily skewed. Examples are also considered that highlight the usefulness of using these approaches to compare location and scale.

In this paper, we assess the effect of tuberculosis pericarditis treatment (prednisolone) on CD4 count changes over time and draw inferences in the presence of missing data. We accounted for the missing data and performed sensitivity analyses to assess robustness of inferences, from a model that assumes that the data are missing at random, to models that assume that the data are not missing at random. Our sensitivity approaches are within the shared-parameter model framework. We implemented the approach by Creemers and colleagues to the CD4 count data and performed simulation studies to evaluate the performance of this approach. We also assessed the influence of potentially influential subjects, on parameter estimates, via the global influence approach. Our results revealed that inferences from missing at random analysis model are robust to not missing at random models and influential subjects did not overturn the study conclusions about prednisolone effect and missing data mechanism. Prednisolone was found to have no significant effect on CD4 count changes over time and also did not interact with anti-retroviral therapy. The simulation studies produced unbiased estimates of prednisolone effect with lower mean square errors and coverage probabilities approximately equal the nominal coverage probability.

In this article, we obtain maximum likelihood and Bayes estimates of the parameters, reliability and hazard functions for generalized Rayleigh distribution when progressive type-II censored sample ...

A multicenter trial is often applied to facilitate recruiting patients into a trial and enhance the generalizability of results to a population. Under a distribution-free random effects log...

The sequential parallel comparison designhas recently been considered to solve the problem with high placebo response and the required sample size in the psychiatric clinical trials. One feature with this design is that a difference between the placebo group and the drug group may also arise in the variance-covariance structure of the clinical outcome. Provided the heterogeneity of the second moment, the treatment effect estimation at the second stage can be biased for the entire randomized patient population that includes patient responders. Our work presented here aims at how the coverage probability of the interval estimation of treatment effect performs under the unstructured variance-covariance matrix. The interaction between the truncation after the first stage and the heterogeneity of the second moment causes a substantial coverage probability problem. The type I error probability may not be controlled under the weak null due to this bias. This bias can also cause spurious power evaluation under an alternative hypothesis. The coverage probability of the ordinary least square statistic is shown in different scenarios.

In this paper, reliability comparison indices are developed for log-normally distributed populations. In this regard, three indices are proposed for reliability comparison of products respectively ...

Process capability indices (PCIs) are widely used to assess whether an in-control process meets manufacturing specifications. In most applications of classical PCIs, the process characteristic is assumed normally distributed. However, the normal distribution has been found inappropriate in various applications. In the literature, the percentile-based PCIs are widely used to deal with the nonnormal process. One problem associated with the percentile-based PCIs is that they do not provide a quantitative interpretation to the process capability. In this study, new PCIs that have a consistent quantification to the process capability for both normal and nonnormal processes are proposed. The proposed PCIs are generalizations of the classical normal PCIs in the sense that they are the same as the classical PCIs when the process characteristic follows a normal distribution, and they offer the same interpretation to the process capability as the classical PCIs when the process characteristic is nonnormal. We then discuss nonparametric and parametric estimation of the proposed PCIs. The nonparametric estimator is based on the kernel density estimation and confidence limits are obtained by the nonparametric bootstrap, while the parametric estimator is based on the maximum likelihood estimation and confidence limits are constructed by the method of generalized pivots. The proposed methodologies are demonstrated using a real example from a manufacturing factory.

Inverse sampling is an appropriate design for the second phase of capture-recapture experiments which provides an exactly unbiased estimator of the population size. However, the sampling distribution of the resulting estimator tends to be highly right skewed for small recapture samples, so, the traditional Wald-type confidence intervals appear to be inappropriate. The objective of this paper is to study the performance of interval estimators for the population size under inverse recapture sampling without replacement. To this aim, we consider the Wald-type, the logarithmic transformation-based, the Wilson score, the likelihood ratio and the exact methods. Also, we propose some bootstrap confidence intervals for the population size, including the with-replacement bootstrap (BWR), the without replacement bootstrap (BWO), and the Rao–Wu’s rescaling method. A Monte Carlo simulation is employed to evaluate the performance of suggested methods in terms of the coverage probability, error rates and standa...

Determining whether there are differential treatment effects in subgroups of trial participants remains an important topic in clinical trials as precision medicine becomes ever more relevant. Any assessment of differential treatment effect is predicated on being able to estimate the treatment response accurately while satisfying constraints of balancing the risk of overlooking an important subgroup with the potential to make a decision based on a false discovery. While regression models, such as marginal interaction model, have been widely used to improve accuracy of subgroup parameter estimates by leveraging the relationship between treatment and covariate, there is still a possibility that it can lead to excessively conservative or anti-conservative results. Conceivably, this can be due to the use of the normal distribution as a default prior, which forces outlying subjects to have their means over-shrunk towards the population mean, and the data from such subjects may be excessively influential in estimation of both the overall mean response and the mean response for each subgroup, or a model mis-specification. To address this issue, we investigate the use of nonparametric Bayes, particularly Dirichlet process priors, to create semi-parametric models. These models represent uncertainty in the prior distribution for the overall response while accommodating heterogeneity among individual subgroups. They also account for the effect and variation due to the unaccounted terms. As a result, the models do not force estimates to excessively shrink but still retain the attractiveness of improved precision given by the narrower credible intervals. This is illustrated in extensive simulations investigating bias, mean squared error, coverage probability and credible interval widths. We applied the method on a simulated data based closely on the results of a cystic fibrosis Phase 2 trial.

The problem of constructing prediction intervals (PIs) for a future sample from a hypergeometric distribution is addressed. Simple closed-form approximate PIs based on the Wald approach, th...

Under an incomplete block crossover design with two periods, we derive the least-squares estimators for the period effect, treatment effects and carry-over effects in explicit formulae based on wit...

This paper utilizes the modified signed log-likelihood ratio method for the problem of inference about the common coefficient of variation in several independent normal populations. This method is ...

Improved point and interval estimation of the smallest scale parameter of n independent populations following two-parameter exponential distributions are studied. The model is formulated in such a way that allows for treating the estimation of the smallest scale parameter as a problem of estimating an unrestricted scale parameter in the presence of a nuisance parameter. The classes of improved point and interval estimators are enriched with Stein-type, Brewster and Zidek-type, Maruyama-type and Strawderman-type improved estimators under both quadratic and entropy losses, whereas using as a criterion the coverage probability, with Stein-type, Brewster and Zidek-type, and Maruyama-type improved intervals. The sampling framework considered incorporates important life-testing schemes such as i.i.d. sampling, type-II censoring, progressive type-II censoring, adaptive progressive type-II censoring, and record values.

The correlation coefficient (CC) is a standard measure of a possible linear association between two continuous random variables. The CC plays a significant role in many scientific disciplines. For ...

In addition to point estimate for the probability of response in a two-stage design (e.g., Simon’s two-stage design for a Phase II clinical trial with binary endpoints), confidence limits should be Cute the confidence interval does not guarantee coverage probability in a two-stage setting. The existing exact approach to calculate one-sided limits is based on the overall number of responses to order the sample space. This approach could be conservative because many sample points have the same limits. We propose a new exact one-sided interval based on p-value for the sample space ordering. Exact intervals are computed by using binomial distributions directly, instead of a normal approximation. Both exact intervals preserve the nominal confidence level. The proposed exact interval based on the p-value generally performs better than the other exact interval with regard to expected length and simple average length of confidence intervals. Therefore, the new interval calculation based on p-value is recommended for use in practice.

In this paper, we consider Marshall–Olkin extended exponential (MOEE) distribution which is capable of modelling various shapes of failure rates and aging criteria. The purpose of this paper is three fold. First, we derive the maximum likelihood estimators of the unknown parameters and the observed the Fisher information matrix from progressively type-II censored data. Next, the Bayes estimates are evaluated by applying Lindley’s approximation method and Markov Chain Monte Carlo method under the squared error loss function. We have performed a simulation study in order to compare the proposed Bayes estimators with the maximum likelihood estimators. We also compute 95% asymptotic confidence interval and symmetric credible interval along with the coverage probability. Third, we consider one-sample and two-sample prediction problems based on the observed sample and provide appropriate predictive intervals under classical as well as Bayesian framework. Finally, we analyse a real data set to illustrate...

Degradation data are an important source of product reliability information. Two popular stochastic models for degradation data are the Gamma process and the inverse Gaussian (IG) process, both of which possess monotone degradation paths. Although these two models have been used in numerous applications, the existing interval estimation methods are either inaccurate given a moderate sample size of the degradation data or require a significant computation time when the size of the degradation data is large. To bridge this gap, this article develops a general framework of interval estimation for the Gamma and IG processes based on the method of generalized pivotal quantities. Extensive simulations are conducted to compare the proposed methods with existing methods under moderate and large sample sizes. Degradation data from capacitors are used to illustrate the proposed methods.

Under a two-parameter exponential distribution, this study constructs the generalized lower confidence limit of the lifetime performance index CL based on type-II right-censored data. The confidenc...

The problems of estimating the mean and an upper percentile of a lognormal population with nonnegative values are considered. For estimating the mean of a such population based on data that include...

The purpose of this article was two-fold (1) provide an overview of the commonly reported and under-reported absolute agreement indices in the kinesiology literature for continuous data; and (2) present examples of these indices for hypothetical data along with recommendations for future use. It is recommended that three types of information be reported as evidence for agreement because no one type is superior to another. Report one graphical display (bivariate plot of raw scores with identity line or Bland-Altman plot), one scaled index (intraclass correlation coefficient with agreement definition or Lin’s Concordance Correlation Coefficient), and at least one unscaled index (root mean squared deviation, total deviation index, coverage probability, or limits of agreement) when there are two methods/raters with no replication. The amount of information recommended exceeds what has commonly been reported in absolute agreement studies published in the kinesiology literature.

This study develops inferential procedures for a gamma distribution. Based on the Cornish–Fisher expansion and pivoting the cumulative distribution function, an approximate confidence interval for ...

In this paper, we consider three distribution-free confidence intervals for quantiles given joint records from two independent sequences of continuous random variables with a common continuous distribution function. The coverage probabilities of these intervals are compared. We then compute the universal bounds of the expected widths of the proposed confidence intervals. These results naturally extend to any number of independent sequences instead of just two. Finally, the proposed confidence intervals are applied for a real data set to illustrate the practical usefulness of the procedures developed here.

The interval between two prespecified order statistics of a sample provides a distribution-free confidence interval for a population quantile. However, due to discreteness, only a small set of exact coverage probabilities is available. Interpolated confidence intervals are designed to expand the set of available coverage probabilities. However, we show here that the infimum of the coverage probability for an interpolated confidence interval is either the coverage probability for the inner interval or the coverage probability obtained by removing the more likely of the two extreme subintervals from the outer interval. Thus, without additional assumptions, interpolated intervals do not expand the set of available guaranteed coverage probabilities.

Defect inspection is important in many industries, such as in the manufacturing and pharmaceutical industries. Existing methods usually use either low-resolution data, which are obtained from less precise measurements, or high-resolution data, which are obtained from more precise measurements, to estimate the number of defectives in a given amount of goods produced. In this study, a novel approach is proposed that combines the two types of data to construct tolerance intervals with a desired average coverage probability. A simulation study shows that the derived tolerance intervals can lead to better performance than a tolerance interval that is constructed based on only the low-resolution data. In addition, a real-data example shows that the tolerance interval based on only the low-resolution data is more conservative than the tolerance intervals based on both high-resolution and low-resolution data.

The problems of interval estimating the mean, quantiles, and survival probability in a two-parameter exponential distribution are addressed. Distribution function of a pivotal quantity whose percen...

We investigate the exact coverage and expected length properties of the model averaged tail area (MATA) confidence interval proposed by Turek and Fletcher, CSDA, 2012, in the context of two nested,...

This article presents parametric bootstrap (PB) approaches for hypothesis testing and interval estimation for the regression coefficients of panel data regression models with incomplete panels. Som...

The mean past lifetime (MPL) function (also known as the expected inactivity time function) is of interest in many fields such as reliability theory and survival analysis, actuarial studies and forensic science. For estimation of the MPL function some procedures have been proposed in the literature. In this paper, we give a central limit theorem result for the estimator of MPL function based on a right-censored random sample from an unknown distribution. The limiting distribution is used to construct normal approximation-based confidence interval for MPL. Furthermore, we use the empirical likelihood ratio procedure to obtain confidence interval for the MPL function. These two intervals are compared with each other through simulation study in terms of coverage probability. Finally, a couple of numerical example illustrating the theory is also given.

In this paper, we focus on exact inference for exponential distribution under multiple Type-I censoring, which is a general form of Type-I censoring and represents that the units are terminated at different times. The maximum likelihood estimate of mean parameter is calculated. Further, the distribution of maximum likelihood estimate is derived and it yields an exact lower confidence limit for the mean parameter. Based on a simulation study, we conclude that the exact limit outperforms the bootstrap limit in terms of the coverage probability and average limit. Finally, a real dataset is analyzed for illustration.

Making predictions of future realized values of random variables based on currently available data is a frequent task in statistical applications. In some applications, the interest is to obtain a two-sided simultaneous prediction interval (SPI) to contain at least k out of m future observations with a certain confidence level based on n previous observations from the same distribution. A closely related problem is to obtain a one-sided upper (or lower) simultaneous prediction bound (SPB) to exceed (or be exceeded) by at least k out of m future observations. In this paper, we provide a general approach for computing SPIs and SPBs based on data from a particular member of the (log)-location-scale family of distributions with complete or right censored data. The proposed simulation-based procedure can provide exact coverage probability for complete and Type II censored data. For Type I censored data, our simulation results show that our procedure provides satisfactory results in small samples. We us...

The article considers the problem of estimating linear parameters in stochastic regression models with Gaussian noises, such as an autoregression of the first order, threshold autoregression, and some others. We propose the non-asymptotic technique for constructing a fixed-size confidence region for unknown parameters with any prescribed coverage probability. The construction makes use of some new properties of the sequential point estimates known in the literature. The results of Monte Carlo simulations for AR(1) and TAR(1) models are given. A new version of the sequential point estimate is proposed.

This study develops methods for constructing some important statistical limits of a gamma distribution. First, we construct upper prediction limits and tolerance limits for a gamma distribution. In addition, upper prediction limits for at least p of m m..

A test procedure for testing homogeneity of location parameters against simple ordered alternative is proposed for k(k ≥ 2) members of two parameter exponential distribution under unbalanced data and heteroscedasticity of the scale parameters. The relevant one-sided and two-sided simultaneous confidence intervals (SCIs) for all k(k − 1)/2 ordered pairwise differences of location parameters are also proposed. Simulation-based study revealed that the proposed procedure is better than the recently proposed procedure in terms of power, coverage probability, and average volume of SCIs. The implementation of proposed procedure is demonstrated through real life data.

There exist various methods for providing confidence intervals for unknown parameters of interest on the basis of a random sample. Generally, the bounds are derived from a system of non-linear equations. In this article, we present a general solution to obtain an unbiased confidence interval with confidence coefficient 1 − α in one-parameter exponential families. Also we discuss two Bayesian credible intervals, the highest posterior density (HPD) and relative surprise (RS) credible intervals. Standard criteria like the coverage length and coverage probability are used to assess the performance of the HPD and RS credible intervals. Simulation studies and real data applications are presented for illustrative purposes.

To construct confidence regions for the difference of two population means, Liu and Yu (2010) proposed a two-sample adjusted empirical likelihood (AEL) with high-order precision. However, two issues have not been well addressed. The first one is that the AEL ratio function is bounded such that the size of the confidence regions may overly expand when the sample sizes are small and/or the dimension of data is large. The second issue is that its high-order precision relies on accurate estimation of the Bartlett factor, while accurately estimating the Bartlett factor is a serious challenge. In order to address these two problems simultaneously, we propose a two-sample modified AEL to ensure the boundedness of confidence regions and preserve the Bartlett correctability. A two-stage procedure is proposed for constructing accurate confidence regions via resampling. The finite-sample performance of the proposed method is illustrated by simulations and a real-data example.