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In this paper, we consider the problem of classification of misaligned multivariate functional data. We propose to use a model-based approach for the joint registration and classification of such data. The observed functional inputs are modeled as a functional nonlinear mixed effects model containing a nonlinear functional fixed effect constructed upon warping functions to account for curve alignment, and a nonlinear functional random effects component to address the variability among subjects. The warping functions are also modeled to accommodate common effect within groups and the variability between subjects. Then, a functional logistic regression model defined upon the representation of the aligned curves and scalar inputs is used to account for curve classification. EM-based algorithms are developed to perform maximum likelihood inference of the proposed models. The identifiability of the registration model and the asymptotical properties of the proposed method are established. The performance of the proposed procedure is illustrated via simulation studies and an analysis of a hyoid bone movement data application. The statistical developments proposed in this paper were motivated by the hyoid bone movement study, the methodology is designed and presented generality and can be applied to numerous areas of scientific research. [ABSTRACT FROM AUTHOR]

In many situations, it is common to have more than one observation per experimental unit, thus generating the experiments with repeated measures. In the modeling of such experiments, it is necessary to consider and model the intra-unit dependency structure. In the literature, there are several proposals to model positive continuous data with repeated measures. In this paper, we propose one more with the generalization of the beta prime regression model. We consider the possibility of dependence between observations of the same unit. Residuals and diagnostic tools also are discussed. To evaluate the finite-sample performance of the estimators, using different correlation matrices and distributions, we conducted a Monte Carlo simulation study. The methodology proposed is illustrated with an analysis of a real data set. Finally, we create an R package for easy access to publicly available the methodology described in this paper. [ABSTRACT FROM AUTHOR]

Clustered current status data are frequently encountered in biomedical research and other areas that require survival analysis. This paper proposes graphical and formal model assessment procedures to evaluate the goodness of fit of the additive hazards model to clustered current status data. The test statistics proposed are based on sums of martingale-based residuals. Relevant asymptotic properties are established, and empirical distributions of the test statistics can be simulated utilizing Gaussian multipliers. Extensive simulation studies confirmed that the proposed test procedures work well for practical scenarios. This proposed method applies when failure times within the same cluster are correlated, and in particular, when cluster sizes can be informative about intra-cluster correlations. The method is applied to analyze clustered current status data from a lung tumorigenicity study. [ABSTRACT FROM AUTHOR]

Among the models applied to analyze survival data, a standout is the inverse Gaussian distribution, which belongs to the class of models to analyze positive asymmetric data. However, the variance of this distribution depends on two parameters, which prevents establishing a functional relation with a linear predictor when the assumption of constant variance does not hold. In this context, the aim of this paper is to re-parameterize the inverse Gaussian distribution to enable establishing an association between a linear predictor and the variance. We propose deviance residuals to verify the model assumptions. Some simulations indicate that the distribution of these residuals approaches the standard normal distribution and the mean squared errors of the estimators are small for large samples. Further, we fit the new model to hospitalization times of COVID-19 patients in Piracicaba (Brazil) which indicates that men spend more time hospitalized than women, and this pattern is more pronounced for individuals older than 60 years. The re-parameterized inverse Gaussian model proved to be a good alternative to analyze censored data with non-constant variance. [ABSTRACT FROM AUTHOR]

Local Linear Regression (LLR) is a nonparametric regression model applied in the modeling phase of Response Surface Methodology (RSM). LLR does not make reference to any fixed parametric model. Hence, LLR is flexible and can capture local trends in the data that might be too complicated for the OLS. However, besides the small sample size and sparse data which characterizes RSM, the performance of the LLR model nosedives as the number of explanatory variables considered in the study increases. This phenomenon, popularly referred to as curse of dimensionality, results in the scanty application of LLR in RSM. In this paper, we propose a novel locally adaptive bandwidths selector, unlike the fixed bandwidths and existing locally adaptive bandwidths selectors, takes into account both the number of the explanatory variables in the study and their individual values at each data point. Single and multiple response problems from the literature and simulated data were used to compare the performance of the L L R P A B with those of the OLS, L L R F B and L L R A B . Neural network activation functions such ReLU, Leaky-ReLU, SELU and SPOCU was considered and give a remarkable improvement on the loss function (Mean Squared Error) over the regression models utilized in the three data. [ABSTRACT FROM AUTHOR]

In recent decades, the use of regression models with random effects has made great progress. Among these models' attractions is the flexibility to analyze correlated data. In various situations, the distribution of the response variable presents asymmetry or bimodality. In these cases, it is possible to use the normal regression with random effect at the intercept. In light of these contexts, i.e. the desire to analyze correlated data in the presence of bimodality or asymmetry, in this paper we propose a regression model with random effect at the intercept based onthe generalized inverse Gaussian distribution model with correlated data. The maximum likelihood is adopted to estimate the parameters and various simulations are performed for correlated data. A type of residuals for the new regression is proposed whose empirical distribution is close to normal. The versatility of the new regression is demonstrated by estimating the average price per hectare of bare land in 10 municipalities in the state of São Paulo (Brazil). In this context, various databases are constantly emerging, requiring flexible modeling. Thus, it is likely to be of interest to data analysts, and can make a good contribution to the statistical literature. [ABSTRACT FROM AUTHOR]

In this paper, by virtual of the inverse probability weighted technique, we considered the jump-preserving estimation on the nonparametric regression models with missing data on response variable. First, we used local piecewise-linear expansion respectively with left and right kernel to approximate the unknown regression function. Second, we obtained the left- and right-limit estimation of regression function at each observed points and then determinated the final estimators by residual sums of squares. Third, we presented the convergence rate of estimators and the residual sums of squares. Finally, we illustrated the performance of our proposed method through some simulation studies and a conjunctivitis example from The Affiliated Hospital of Hangzhou Normal University. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new distribution, named unit log–log distribution, defined on the bounded (0,1) interval. Basic distributional properties such as model shapes, stochastic ordering, quantile function, moments, and order statistics of the newly defined unit distribution are studied. The maximum likelihood estimation method has been pointed out to estimate its model parameters. The new quantile regression model based on the proposed distribution is introduced and it has been derived estimations of its model parameters also. The Monte Carlo simulation studies have been given to see the performance of the estimation method based on the new unit distribution and its regression modeling. Applications of the newly defined distribution and its quantile regression model to real data sets show that the proposed models have better modeling abilities than competitive models. The proposed unit quantile regression model has targeted to explain linear relation between educational measurements of both OECD (Organization for Economic Co-operation and Development) countries and some non-members of OECD countries, and their Better Life Index. The existence of the significant covariates has been seen on the real data applications for the unit median response. [ABSTRACT FROM AUTHOR]

Researchers in statistical shape analysis often analyze outlines of objects. Even though these contours are infinite-dimensional in theory, they must be discretized in practice. When discretizing, it is important to reduce the number of sampling points considerably to reduce computational costs, but to not use too few points so as to result in too much approximation error. Unfortunately, determining the minimum number of points needed to achieve sufficiently approximate the contours is computationally expensive. In this paper, we fit regression models to predict these lower bounds using characteristics of the contours that are computationally cheap as predictor variables. However, least squares regression is inadequate for this task because it treats overestimation and underestimation equally, but underestimation of lower bounds is far more serious. Instead, to fit the models, we use the LINEX loss function, which allows us to penalize underestimation at an exponential rate while penalizing overestimation only linearly. We present a novel approach to select the shape parameter of the loss function and tools for analyzing how well the model fits the data. Through validation methods, we show that the LINEX models work well for reducing the underestimation for the lower bounds. [ABSTRACT FROM AUTHOR]

This paper introduces a new class of efficient and debiased two-step shrinkage estimators for a linear regression model in the presence of multicollinearity. We derive the proposed estimators' mean square error and define the necessary and sufficient conditions for superiority over the existing estimators. In addition, we develop an algorithm for selecting the shrinkage parameters for the proposed estimators. The comparison of the new estimators versus the traditional ordinary least squares, ridge regression, Liu, and the two-parameter estimators is done by a matrix mean square error criterion. The Monte Carlo simulation results show the superiority of the proposed estimators under certain conditions. In the presence of high but imperfect multicollinearity, the two-step shrinkage estimators' performance is relatively better. Finally, two real-world chemical data are analyzed to demonstrate the advantages and the empirical relevance of our newly proposed estimators. It is shown that the standard errors and the estimated mean square error decrease substantially for the proposed estimator. Hence, the precision of the estimated parameters is increased, which of course is one of the main objectives of the practitioners. [ABSTRACT FROM AUTHOR]

In this paper, we study the properties of a special class of frailty models when the frailty is common to several failure times. The models are closely linked to Archimedean copula models. We establish a useful formula for cumulative baseline hazard functions and develop a new estimator for cumulative baseline hazard functions in bivariate frailty regression models. Based on our proposed estimator, we present a graphical model checking procedure. We fit a leukemia data set using our model and end our paper with some discussions. [ABSTRACT FROM AUTHOR]

This paper introduces a new class of distributions by compounding the inverse Lindley distribution and power series distributions which is called compound inverse Lindley power series (CILPS) distributions. An important feature of this distribution is that the lifetime of the component associated with a particular risk is not observable, rather only the minimum lifetime value among all risks is observable. Further, these distributions exhibit an unimodal failure rate. Various properties of the distribution are derived. Besides, two special models of the new family are investigated. The model parameters of the two sub-models of the new family are obtained by the methods of maximum likelihood, least square, weighted least square and maximum product of spacing and compared them using the Monte Carlo simulation study. Besides, the log compound inverse Lindley regression model for censored data is proposed. Three real data sets are analyzed to illustrate the flexibility and importance of the proposed models. [ABSTRACT FROM AUTHOR]

According to the Atlas of Human Development in Brazil, the income dimension of Municipal Human Development Index (MHDI-I) is an indicator that shows the population's ability in a municipality to ensure a minimum standard of living to provide their basic needs, such as water, food and shelter. In public policy, one of the research objectives is to identify social and economic variables that are associated with this index. Due to the income inequality, evaluate these associations in quantiles, instead of the mean, could be more interest. Thus, in this paper, we develop a Bayesian variable selection in quantile regression models with hierarchical random effects. In particular, we assume a likelihood function based on the Generalized Asymmetric Laplace distribution, and a spike-and-slab prior is used to perform variable selection. The Generalized Asymmetric Laplace distribution is a more general alternative than the Asymmetric Laplace one, which is a common approach used in quantile regression under the Bayesian paradigm. The performance of the proposed method is evaluated via a comprehensive simulation study, and it is applied to the MHDI-I from municipalities located in the state of Rio de Janeiro. [ABSTRACT FROM AUTHOR]

In the censored data exploration, the classical linear regression model which assumes normally distributed random errors is perhaps one of the commonly used frameworks. However, practical studies have often criticized the classical linear regression model because of its sensitivity to departure from the normality and partial nonlinearity. This paper proposes to solve these potential issues simultaneously in the context of the partial linear regression model by assuming that the random errors follow a scale-mixture of normal (SMN) family of distributions. The postulated method allows us to model data with great flexibility, accommodating heavy tails and outliers. By implementing the B-spline approximation and using the convenient hierarchical representation of the SMN distributions, a computationally analytical EM-type algorithm is developed for obtaining maximum likelihood (ML) parameter estimates. Various simulation studies are conducted to investigate the finite sample properties, as well as the robustness of the model in dealing with the heavy tails distributed datasets. Real-world data examples are finally analyzed for illustrating the usefulness of the proposed methodology. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new kind of multivariate t distribution by allowing different degrees of freedom for each univariate component. Compared with the classical multivariate t distribution, it is more flexible in the model specification that can be used to deal with the variant amounts of tail weights on marginals in multivariate data modeling. In particular, it could include components following the multivariate normal distribution, and it contains the product of independent t-distributions as a special case. Subsequently, it is extended to the regression model as the joint distribution of the error terms. Important distributional properties are explored and useful statistical methods are developed. The flexibility of the specified structure in better capturing the characteristic of data is exemplified by both simulation studies and real data analyses. [ABSTRACT FROM AUTHOR]

The models used to describe the kinetics of ruminal degradation are usually nonlinear models where the dependent variable is the proportion of degraded food. The method of least squares is the standard approach used to estimate the unknown parameters but this method can lead to unacceptable predictions. To solve this issue, a beta nonlinear model and the Bayesian perspective is proposed in this article. The application of standard methodologies to obtain prior distributions, such as the Jeffreys prior or the reference priors, involves serious difficulties here because this model is a nonlinear non-normal regression model, and the constrained parameters appear in the log-likelihood function through the Gamma function. This paper proposes an objective method to obtain the prior distribution, which can be applied to other models with similar complexity, can be easily implemented in OpenBUGS, and solves the problem of unacceptable predictions. The model is generalized to a larger class of models. The methodology was applied to real data with three models that were compared using the Deviance Information Criterion and the root mean square prediction error. A simulation study was performed to evaluate the coverage of the credible intervals. [ABSTRACT FROM AUTHOR]

Linear regression models are useful statistical tools to analyze data sets in different fields. There are several methods to estimate the parameters of a linear regression model. These methods usually perform under normally distributed and uncorrelated errors. If error terms are correlated the Conditional Maximum Likelihood (CML) estimation method under normality assumption is often used to estimate the parameters of interest. The CML estimation method is required a distributional assumption on error terms. However, in practice, such distributional assumptions on error terms may not be plausible. In this paper, we propose to estimate the parameters of a linear regression model with autoregressive error term using Empirical Likelihood (EL) method, which is a distribution free estimation method. A small simulation study is provided to evaluate the performance of the proposed estimation method over the CML method. The results of the simulation study show that the proposed estimators based on EL method are remarkably better than the estimators obtained from CML method in terms of mean squared errors (MSE) and bias in almost all the simulation configurations. These findings are also confirmed by the results of the numerical and real data examples. [ABSTRACT FROM AUTHOR]

In obstetrics and gynecology, knowledge about how women's features are associated with childbirth is important. This leads to establishing guidelines and can help managers to describe the dynamics of pregnant women's hospital stays. Then, time is a variable of great importance and can be described by survival models. An issue that should be considered in the modeling is the inclusion of women for whom the duration of labor cannot be observed due to fetal death, generating a proportion of times equal to zero. Additionally, another proportion of women's time may be censored due to some intervention. The aim of this paper was to present the Log-Normal zero-inflated cure regression model and to evaluate likelihood-based parameter estimation by a simulation study. In general, the inference procedures showed a better performance for larger samples and low proportions of zero inflation and cure. To exemplify how this model can be an important tool for investigating the course of the childbirth process, we considered the Better Outcomes in Labor Difficulty project dataset and showed that parity and educational level are associated with the main outcomes. We acknowledge the World Health Organization for granting us permission to use the dataset. [ABSTRACT FROM AUTHOR]

This paper discusses methods of estimating the reproductive power and the accompanying survival function of communicable events, e.g. infectious disease transmission. The early stage of an outbreak can be described by the infectiousness of the outbreak process, but in later stages of the outbreak, this is complicated by factors such as changing contact patterns and the impact of control measures. It is important to take these factors into account in order to get a good, if approximate, model for an outbreak process. This paper proposes a non-homogeneous birth process and regression model for the reproductive power function, similar to models in discrete survival analysis. A baseline reproductive power function gives a description of the outbreak when covariates are at their baseline values. As an illustration these methods are applied to an avian influenza (H5N1) outbreak among poultry in Thailand. [ABSTRACT FROM AUTHOR]

In this application note paper, we propose and examine the performance of a Bayesian approach for a homoscedastic nonlinear regression (NLR) model assuming errors with two-piece scale mixtures of normal (TP-SMN) distributions. The TP-SMN is a large family of distributions, covering both symmetrical/ asymmetrical distributions as well as light/heavy tailed distributions, and provides an alternative to another well-known family of distributions, called scale mixtures of skew-normal distributions. The proposed family and Bayesian approach provides considerable flexibility and advantages for NLR modelling in different practical settings. We examine the performance of the approach using simulated and real data. [ABSTRACT FROM AUTHOR]

In this paper, we investigate robust parameter estimation and variable selection for binary regression models with grouped data. We investigate estimation procedures based on the minimum-distance approach. In particular, we employ minimum Hellinger and minimum symmetric chi-squared distances criteria and propose regularized minimum-distance estimators. These estimators appear to possess a certain degree of automatic robustness against model misspecification and/or for potential outliers. We show that the proposed non-penalized and penalized minimum-distance estimators are efficient under the model and simultaneously have excellent robustness properties. We study their asymptotic properties such as consistency, asymptotic normality and oracle properties. Using Monte Carlo studies, we examine the small-sample and robustness properties of the proposed estimators and compare them with traditional likelihood estimators. We also study two real-data applications to illustrate our methods. The numerical studies indicate the satisfactory finite-sample performance of our procedures. [ABSTRACT FROM AUTHOR]

In this paper, we consider a regression model under the generalized Waring distribution for modeling count data. We develop and implement local influence diagnostic techniques based on likelihood displacement. Also we develop case-deletion methods. The generalized Waring regression model is presented as a mixture of the Negative Binomial and the Beta II distributions, and it is compared to the Negative Binomial and Waring regression models. Estimation is performed by maximum likelihood function. The influence measures developed in this paper are applied to a Spanish football league data set. Empirical results show that the generalized Waring regression model performs better when compared to the Negative Binomial and Waring regression models. Technical details are presented in the Appendix. [ABSTRACT FROM AUTHOR]

In regression model applications, the errors may frequently present a symmetric shape. In such cases, the normal and Student t distributions are commonly used. In this paper, we shall be concerned only to model heavy-tailed, skewed errors and absence of variance homogeneity with two regression structures based on the skew t distribution. We consider a classic analysis for the parameters of the proposed model. We perform a diagnostic analysis based on global influence and quantile residuals. For different parameter settings and sample sizes, various simulation results are obtained and compared to evaluate the performance of the skew t regression. Further, we illustrate the usefulness of the new regression by means of a real data set (amount of potassium in different soil areas) from a study carried out at the Department of Soil Science of the Luiz de Queiroz School of Agriculture, University of São Paulo. [ABSTRACT FROM AUTHOR]

A special source of difficulty in the statistical analysis is the possibility that some subjects may not have a complete observation of the response variable. Such incomplete observation of the response variable is called censoring. Censorship can occur for a variety of reasons, including limitations of measurement equipment, design of the experiment, and non-occurrence of the event of interest until the end of the study. In the presence of censoring, the dependence of the response variable on the explanatory variables can be explored through regression analysis. In this paper, we propose to examine the censorship problem in context of the class of asymmetric, i.e., we have proposed a linear regression model with censored responses based on skew scale mixtures of normal distributions. We develop a Monte Carlo EM (MCEM) algorithm to perform maximum likelihood inference of the parameters in the proposed linear censored regression models with skew scale mixtures of normal distributions. The MCEM algorithm has been discussed with an emphasis on the skew-normal, skew Student-t-normal, skew-slash and skew-contaminated normal distributions. To examine the performance of the proposed method, we present some simulation studies and analyze a real dataset. [ABSTRACT FROM AUTHOR]

The common approach for regression analysis with compositional variables is to express compositions in log-ratio coordinates (coefficients) and then perform standard statistical processing in real space. Similar to working in real space, the problem is that the standard least squares regression fails when the number of parts of all compositional covariates is higher than the number of observations. The aim of this study is to analyze in detail the partial least squares (PLS) regression which can deal with this problem. In this paper, we focus on the PLS regression between more than one compositional response variable and more than one compositional covariate. First, we give the PLS regression model with log-ratio coordinates of compositional variables, then we express the PLS model directly in the simplex. We also prove that the PLS model is invariant under the change of coordinate system, such as the ilr coordinates with a different contrast matrix or the clr coefficients. Moreover, we give the estimation and inference for parameters in PLS model. Finally, the PLS model with clr coefficients is used to analyze the relationship between the chemical metabolites of Astragali Radix and the plasma metabolites of rat after giving Astragali Radix. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new regression model, called Lomax regression model, as an alternative to the gamma regression model. The maximum-likelihood method is used to estimate the unknown parameters of the proposed model, and the finite sample performance of the maximum-likelihood estimation method is evaluated by means of the Monte-Carlo simulation study. The randomized quantile residuals are used to check the adequacy of the fitted model. The insurance data are analyzed to demonstrate the usefulness of the proposed regression model against the gamma regression model. [ABSTRACT FROM AUTHOR]

Parameters of a linear regression model can be estimated with the help of traditional methods like generalized least squares and mixed estimator. However, recent developments increased the importance of big data sets, which have much more predictors than observations where some predictors have no impact on the dependent variable. The estimation and model selection problem of big datasets can be solved using the least absolute shrinkage and selection operator (Lasso). However, to the authors' knowledge, there is no study that incorporates stochastic restrictions, within a Lasso framework. In this paper, we propose a Mixed Lasso (M-Lasso) estimator that incorporates stochastic linear restrictions to big data sets for selecting the true model and estimating parameters simultaneously. We conduct a simulation study to compare the performance of M-Lasso with existing estimators based on mean squared error (mse) and model selection performance. Results show that M-Lasso is superior in terms of mse and it generally dominates compared estimators according to the model selection criteria. We employ M-Lasso to estimate parameters of a widely analysed production function under stochastic restrictions raised from economic theory. Our results show that M-Lasso can provide reasonable and more precise estimates of model parameters that are in line with the economic theory. [ABSTRACT FROM AUTHOR]

It is well-known that classical Tobit estimator of the parameters of the censored regression (CR) model is inefficient in case of non-normal error terms. In this paper, we propose to use the modified maximum likelihood (MML) estimator under the Jones and Faddy's skew t-error distribution, which covers a wide range of skew and symmetric distributions, for the CR model. The MML estimators, providing an alternative to the Tobit estimator, are explicitly expressed and they are asymptotically equivalent to the maximum likelihood estimator. A simulation study is conducted to compare the efficiencies of the MML estimators with the classical estimators such as the ordinary least squares, Tobit, censored least absolute deviations and symmetrically trimmed least squares estimators. The results of the simulation study show that the MML estimators work well among the others with respect to the root mean square error criterion for the CR model. A real life example is also provided to show the suitability of the MML methodology. [ABSTRACT FROM AUTHOR]

The case-cohort design is widely used as a means of reducing the cost in large cohort studies, especially when the disease rate is low and covariate measurements may be expensive, and has been discussed by many authors. In this paper, we discuss regression analysis of case-cohort studies that produce interval-censored failure time with dependent censoring, a situation for which there does not seem to exist an established approach. For inference, a sieve inverse probability weighting estimation procedure is developed with the use of Bernstein polynomials to approximate the unknown baseline cumulative hazard functions. The proposed estimators are shown to be consistent and the asymptotic normality of the resulting regression parameter estimators is established. A simulation study is conducted to assess the finite sample properties of the proposed approach and indicates that it works well in practical situations. The proposed method is applied to an HIV/AIDS case-cohort study that motivated this investigation. [ABSTRACT FROM AUTHOR]

This paper studies the outlier detection and robust variable selection problem in the linear regression model. The penalized weighted least absolute deviation (PWLAD) regression estimation method and the adaptive least absolute shrinkage and selection operator (LASSO) are combined to simultaneously achieve outlier detection, and robust variable selection. An iterative algorithm is proposed to solve the proposed optimization problem. Monte Carlo studies are evaluated the finite-sample performance of the proposed methods. The results indicate that the finite sample performance of the proposed methods performs better than that of the existing methods when there are leverage points or outliers in the response variable or explanatory variables. Finally, we apply the proposed methodology to analyze two real datasets. [ABSTRACT FROM AUTHOR]

Variable selection in finite mixture of regression (FMR) models is frequently used in statistical modeling. The majority of applications of variable selection in FMR models use a normal distribution for regression error. Such assumptions are unsuitable for a set of data containing a group or groups of observations with asymmetric behavior. In this paper, we introduce a variable selection procedure for FMR models using the skew-normal distribution. With appropriate choice of the tuning parameters, we establish the theoretical properties of our procedure, including consistency in variable selection and the oracle property in estimation. To estimate the parameters of the model, a modified EM algorithm for numerical computations is developed. The methodology is illustrated through numerical experiments and a real data example. [ABSTRACT FROM AUTHOR]

For count responses, there are situations in biomedical and sociological applications in which extra zeroes occur. Modeling correlated (e.g. repeated measures and clustered) zero-inflated count data includes special challenges because the correlation between measurements for a subject or a cluster needs to be taken into account. Moreover, zero-inflated count data are often faced with over/under dispersion problem. In this paper, we propose a random effect model for repeated measurements or clustered data with over/under dispersed response called random effect zero-inflated exponentiated-exponential geometric regression model. The proposed method was illustrated through real examples. The performance of the model and asymptotical properties of the estimations were investigated using simulation studies. [ABSTRACT FROM AUTHOR]

In recent years, a variety of regression models, including zero-inflated and hurdle versions, have been proposed to explain the case of a dependent variable with respect to exogenous covariates. Apart from the classical Poisson, negative binomial and generalised Poisson distributions, many proposals have appeared in the statistical literature, perhaps in response to the new possibilities offered by advanced software that now enables researchers to implement numerous special functions in a relatively simple way. However, we believe that a significant research gap remains, since very little attention has been paid to the quasi-binomial distribution, which was first proposed over fifty years ago. We believe this distribution might constitute a valid alternative to existing regression models, in situations in which the variable has bounded support. Therefore, in this paper we present a zero-inflated regression model based on the quasi-binomial distribution, taking into account the moments and maximum likelihood estimators, and perform a score test to compare the zero-inflated quasi-binomial distribution with the zero-inflated binomial distribution, and the zero-inflated model with the homogeneous model (the model in which covariates are not considered). This analysis is illustrated with two data sets that are well known in the statistical literature and which contain a large number of zeros. [ABSTRACT FROM AUTHOR]

This paper considers the estimation of parameters for the Poisson regression model in the presence of high, but imperfect multicollinearity. To mitigate this problem, we suggest using the Poisson Liu Regression Estimator (PLRE) and propose some new approaches to estimate this shrinkage parameter. The small sample statistical properties of these estimators are systematically scrutinized using Monte Carlo simulations. To evaluate the performance of these estimators, we assess the Mean Square Errors (MSE) and the Mean Absolute Percentage Errors (MAPE). The simulation results clearly illustrate the benefit of the methods of estimating these types of shrinkage parameters in finite samples. Finally, we illustrate the empirical relevance of our newly proposed methods using an empirically relevant application. Thus, in summary, via simulations of empirically relevant parameter values, and by a standard empirical application, it is clearly demonstrated that our technique exhibits more precise estimators, compared to traditional techniques – at least when multicollinearity exist among the regressors. [ABSTRACT FROM AUTHOR]

Stratified regression models are commonly employed when study subjects may come from possibly different strata such as different medical centers, and for the situation, one common question of interest is to test the existence of the stratum effect. To address this, there exists some literature on the testing of the stratum effects under the framework of the proportional hazards model when one observes right-censored data or interval-censored data. In this paper, we consider the situation under the additive hazards model when one faces current status data, for which there does not seem to exist an established test procedure. The asymptotic distributions of the proposed test procedure are provided. Also a simulation study is performed to evaluate the performance of the proposed method and indicates that it works well for practical situations. The approach is applied to a set of real current status data from a tumorigenicity study. [ABSTRACT FROM AUTHOR]

The heteroscedastic nonlinear regression model (HNLM) is an important tool in data modeling. In this paper we propose a HNLM considering skew scale mixtures of normal (SSMN) distributions, which allows fitting asymmetric and heavy-tailed data simultaneously. Maximum likelihood (ML) estimation is performed via the expectation-maximization (EM) algorithm. The observed information matrix is derived analytically to account for standard errors. In addition, diagnostic analysis is developed using case-deletion measures and the local influence approach. A simulation study is developed to verify the empirical distribution of the likelihood ratio statistic, the power of the homogeneity of variances test and a study for misspecification of the structure function. The method proposed is also illustrated by analyzing a real dataset. [ABSTRACT FROM AUTHOR]

Regression analyses are commonly performed with doubly limited continuous dependent variables; for instance, when modeling the behavior of rates, proportions and income concentration indices. Several models are available in the literature for use with such variables, one of them being the unit gamma regression model. In all such models, parameter estimation is typically performed using the maximum likelihood method and testing inferences on the model's parameters are usually based on the likelihood ratio test. Such a test can, however, deliver quite imprecise inferences when the sample size is small. In this paper, we propose two modified likelihood ratio test statistics for use with the unit gamma regressions that deliver much more accurate inferences when the number of data points in small. Numerical (i.e. simulation) evidence is presented for both fixed dispersion and varying dispersion models, and also for tests that involve nonnested models. We also present and discuss two empirical applications. [ABSTRACT FROM AUTHOR]

Many phenomena exist in the space–time domain, often with a low data sampling rate and sparsely distributed network of observed points. Therefore, spatio-temporal interpolation with high accuracy is necessary. In this paper, a space–time regression-kriging model was introduced and applied to monthly average temperature data. First, a time series decomposition was applied for each station, and a multiple linear regression model was used to fit space–time trends. Second, a valid nonseparable spatio-temporal variogram function was utilized to describe similarities of the residuals in space–time. Finally, space–time kriging was applied to predict monthly air temperature. Jackknife techniques were used to predict the monthly temperature at all stations, with correlation coefficients between predictions and observed data very close to 1. Moreover, to evaluate the advantages of space–time kriging, pure time forecasting also was executed employing an autoregressive integrated moving average (ARIMA) model. The results of these two methods show that both mean absolute error (MAE) and root-mean-square error (RMSE) of space–time prediction are much lower than those of the pure time forecasting. The estimated temperature curves for stations also show that the former present a conspicuous improvement in interpolation accuracy when compared with the latter. [ABSTRACT FROM AUTHOR]

The Beta distribution is the standard model for quantifying the influence of covariates on the mean of a response variable on the unit interval. However, this well-known distribution is no longer useful when we are interested in quantifying the influence of such covariates on the quantiles of the response variable. Unlike Beta, the Kumaraswamy distribution has a closed-form expression for its quantile and can be useful for the modeling of quantiles in the absence/presence of covariates. As an alternative to the Kumaraswamy distribution for the modeling of quantiles, in this paper the unit-Weibull distribution was considered. This distribution was obtained by the transformation of a random variable with Weibull distribution. The same transformation applied to a random variable with Exponentiated Exponential distribution generates the Kumaraswamy distribution. The suitability of our proposal was demonstrated to model quantiles, conditional on covariates, with two simulated examples and three real applications with datasets from health, accounting and social science. For such data sets, the obtained fits of the proposed regression model were compared with those provided by the Beta and Kumaraswamy regression models. [ABSTRACT FROM AUTHOR]

In a note about the paper titled 'On the one parameter unit-Lindley distribution and its associated regression model for proportion data', Mazucheli et al. [J. Appl. Stat. 46 (2019), pp. 700–714] and Nadarajah and Chan [On moments of the unit Lindley distribution, J. Appl. Stat. (under review)] claim that 'The expressions given for the moments and incomplete moments are not correct and not in closed form'. While we agree that they are not in closed form and observe a typo in the expressions for μ k ′ and T k (t) , k = 1 , ... , the expressions for μ 1 ′ , μ 2 ′ , μ 3 ′ and μ 4 ′ are, however, entirely correct. [ABSTRACT FROM AUTHOR]

This paper proposes a new regression model for the analysis of spatial panel data in the case of spatial heterogeneity and non-normality. In empirical economic research, the normality of error components is a routine assumption for the models with continuous responses. However, such an assumption may not be appropriate in many applications. This work relaxes the normality assumption by using a multivariate skew-normal distribution, which includes the normal distribution as a special case. The methodology is illustrated through a simulation study and application to insurance and gasoline demand data sets. In these analyses, a simple Bayesian framework that implements a Markov chain Monte Carlo algorithm is derived for parameter estimation and inference. [ABSTRACT FROM AUTHOR]

Providing reliable estimates of subpopulation/area parameters has attracted increased attention due to their importance in applications such as policymaking. Due to low or even no samples from some areas, we must adopt indirect model approaches. Existing indirect small area estimation methods often assume that a single nested error regression model is suitable for all the small areas. In particular, the effects of the auxiliary variables are either fixed or have a single attraction center. In some applications, it can be more appropriate to cluster the small areas so that the effects of the auxiliary variables are fixed but have multiple centers in the nested error regression model. In this paper, we examine an extended nested error regression model in which the auxiliary variables have mixed effects with multiple centers. We use a penalty approach to identify these centers and estimate the model parameters simultaneously. We then propose two new small area mean estimators and construct estimators of their mean square errors. Simulations based on artificial and realistic finite populations show that the new estimators can be efficient. Furthermore, the confidence intervals based on the new methods have accurate coverage probabilities. We illustrate the proposed methods with the Survey of Labour and Income Dynamics conducted in Canada. [ABSTRACT FROM AUTHOR]

To handle the multicollinearity issues in the regression analysis, a class of 'strictly concave penalty function' is described in this paper. As an example, a new penalty function called 'modified log penalty' is introduced. The penalized estimator based on strictly concave penalties enjoys the oracle property under certain regularity conditions discussed in the literature. In the multicollinearity cases where such conditions are not applicable, the behaviors of the strictly concave penalties are discussed through examples involving strongly correlated covariates. Real data examples and simulation studies are provided to show the finite-sample performance of the modified log penalty in terms of prediction error under scenarios exhibiting multicollinearity. [ABSTRACT FROM AUTHOR]

Time lag effect exists widely in the course of economic operation. Some economic variables are affected not only by various factors in the current period but also by various factors in the past and even their own past values. As a class of dynamical models, autoregressive distributed lag (ARDL) models are frequently used to conduct dynamic regression analysis. In this paper, we are interested in the quantile regression (QR) modeling of the ARDL model in a dynamic framework. By combining the working likelihood of asymmetric Laplace distribution (ALD) with the expectation–maximization (EM) algorithm into the considered ARDL model, the iterative weighted least square estimators (IWLSE) are derived. Some Monte Carlo simulations are implemented to evaluate the performance of the proposed estimation method. A dataset of the consumption of electricity by residential customers is analyzed to illustrate the application. [ABSTRACT FROM AUTHOR]

This paper considers the quantile regression model with both individual fixed effect and time period effect for general spatial panel data. Fixed effects quantile regression estimators based on instrumental variable method will be proposed. Asymptotic properties of the proposed estimators will be developed. Simulations are conducted to study the performance of the proposed method. We will illustrate our methodologies using a cigarettes demand data set. [ABSTRACT FROM AUTHOR]