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In this paper, the seven equivalent conditions of complete moment convergence and complete integral convergence for m -asymptotic negatively associated ( m -ANA, for short) random variables are established. The results obtained in the paper extend and improve some corresponding ones for negatively associated (NA, for short) random variables and negatively orthant dependent (NOD, for short) random variables. As an application of our main results, we present a result on complete consistency for the weighted estimator in a nonparametric regression model based on m-ANA errors. We perform a numerical simulation to verify the validity of the theoretical results. [ABSTRACT FROM AUTHOR]

Recently, providing a new count regression model is very popular for many researchers. These count regression models are constructed by using a new discrete distribution or one of the existing distributions in the literature. In this paper, we consider a new zero-inflated regression model as an alternative to the zero-inflated regression models. We present two real data applications to illustrate the usefulness of the suggested regression model in modeling data, and compare the competitor models such as Poisson, discrete Lindley, and zero-inflated regression models. We provide a new count regression model which is useful in modeling overdispersed data. [ABSTRACT FROM AUTHOR]

The problem of constructing locally D-optimal designs for two-variable logistic model with no interaction has been studied in many literature. In Kabera, Haines, and Ndlovu (2015), the model is restricted to have positive slopes and negative intercept for the assumptions that the probability of response increases with doses for both drugs and that the probability of response is less than 0.5 at zero dose level of both drugs. The design space mainly discussed is the set [ 0 , ∞) × [ 0 , ∞) , while the finite rectangular design space is presented only in scenarios where the results for the unlimited design space are still appropriate. In this paper, we intend to loose these restrictions and discuss the rectangular design spaces for the model where the D-optimal designs can not be obtained. The result can be extended to the models where drugs have negative or opposite effects, or the models with positive intercept, by using translation and reflection in the first quadrant. [ABSTRACT FROM AUTHOR]

In this paper, the complete convergence for maximum of weighted sums of widely negative orthant dependent (WNOD) random variables are investigated. Some sufficient conditions for the convergence are provided and a relationship between the weight and the boundary function is revealed. Additionally, a Marcinkiewicz-Zygmund type strong law of large number for weighted sums of WNOD random variables is obtained. The results obtained in this paper generalize some corresponding ones for independent and some dependent random variables. As an application, the strong consistency for the weighted estimator in a non-parametric regression model is established. MR(2010) Subject Classification: 60F15; 62G05. [ABSTRACT FROM AUTHOR]

In this paper, we propose a MIXED penalty for the LAD regression model, which can estimate parameters and select important variables efficiently and stably. The proposed method has a good performance in the case of dependent variable with heavy tail and outliers, so this estimator is robust and efficient for tackling the problem of heterogeniety. We show that the proposed estimator possesses the good properties by applying certain assumptions. In the part of numerical simulation, we give several simulation studies to examine the asymptotic results, which shows that the method we proposed behaves better. [ABSTRACT FROM AUTHOR]

Variable selection approaches are often employed in high-dimensionality and multicollinearity problems. Since lasso selects variables by shrinking the coefficients, it has extensive use in many fields. On the other, we may sometime have extra information on the model. In this case, the extra information should be considered in the estimation procedure. In this paper, we propose a stochastic restricted lasso estimator in linear regression model which uses the extra information as stochastic linear restrictions. The estimator is a generalization of mixed estimator with L1 type penalization. We give the coordinate descent algorithm to estimate the coefficient vector of the proposed method and strong rules for the coordinate descent algorithm to discard variables from the model. Also, we propose a method to estimate the tuning parameter. We conduct two real data analyses and simulation studies to compare the new estimator with several estimators including the ridge, lasso and stochastic restricted ridge. The real data analyses and simulation studies show that the new estimator enjoys the automatic variable selection property of the lasso while outperforms standard methods, achieving lower test mean squared error. [ABSTRACT FROM AUTHOR]

The penalized regression is an important technique for high-dimensional data analysis, but penalized estimation method hinge on finding a suitable choice of tuning parameter. In this paper, a simple modified L curve method is proposed to select the tuning parameter for penalized estimation including Lasso, SCAD and MCP in linear regression models. Through data simulation and actual data analysis, we find that the modified L curve method can be simpler and more accurate than traditional tuning parameter selection schemes such as CV and BIC. Furthermore, the method is able to identify the true model consistently and has the less model error, especially for the cases where there is a high correlation between predictors. [ABSTRACT FROM AUTHOR]

This paper considers nonlinear regression models when neither the response variable nor the covariates can be directly observed, but are measured with exponential parametric distortion measurement errors. To estimate parameters in the distortion functions, we propose nonlinear least squares and weighted nonlinear least squares estimation methods under two identifiability conditions. After obtaining calibrated variables, the nonlinear least squares based estimators are proposed to estimate the parameters in the regression model. We studied the asymptotic results of estimators, especially we discuss the difference between the parametric calibrations and nonparametric calibrations. The latter is conducted as if the parametric structures in distortion functions are unknown. Simulation studies demonstrate the performance of the proposed estimators. [ABSTRACT FROM AUTHOR]

In this paper, we discuss some theoretical results and properties of a discrete version of the Birnbaum-Saunders distribution. We present a proof of the unimodality of this model. Moreover, results on moments, quantile function, reliability and order statistics are also presented. In addition, we propose a regression model based on the discrete Birnbaum-Saunders distribution. The model parameters are estimated by the maximum likelihood method and a Monte Carlo study is performed to evaluate the performance of the estimators. Finally, we illustrate the proposed methodology with the use of real data sets. [ABSTRACT FROM AUTHOR]

This paper establishes an Edgeworth expansion for the t-statistic of the Whittle Maximum Likelihood Estimator (WMLE) of a linear regression model whose residual component is stationary, Gaussian, and strongly dependent time series. Under the widely used set of assumptions and two more mild additional conditions on the spectral density function and the parametric values, an Edgeworh expansion of the t-statistic of arbitrarily large order of the process is proved to have an error of o (n 1 − s / 2) where s is a positive integer. [ABSTRACT FROM AUTHOR]

This paper focuses on nonparametric regression modeling of time-series and incomplete observations. In this sense, the observations are subject to both left truncation and right censoring (LTRC) and satisfy an association dependency. Using the well-known kernel estimation method, we establish the strong uniform consistency with a rate of the kernel estimator proposed in this paper. Simulation studies are conducted to assess the impact of both incompleteness and association dependency on the estimation. [ABSTRACT FROM AUTHOR]

The consistency of the semi-parametric maximum likelihood estimator (SMLE) under the semi-parametric linear regression model with right-censoring data (SPLRRC model) has not been studied under the necessary and sufficient condition for the identifiability of the parameters. In this paper, we discuss the necessary and sufficient condition for the consistency of SMLE under type I right censoring. [ABSTRACT FROM AUTHOR]

By establishing a connection between a quantile regression and an asymmetric Laplace distribution (ALD), this paper considers the maximum likelihood estimation of parameters of a quantile autoregression model with Markovian switching (MSQAR), where the error terms obey ALD whose scale parameter depends on regime shifts. By utilizing the mixture representation of ALD, we develop an effective ML approach for estimating parameters of MSQAR models, and obtain closed-form estimators of unknown parameters via the EM algorithm. Consistency and asymptotic normality of estimators are shown by extending some techniques adopted in Douc, Moulines, and Rydén (2004). Also, we extend some asymptotic results of estimators to the case where the conditional quantile regression model is misspecified. Furthermore, the proposed approach is illustrated by simulations and empirical data. Simulation results show that the procedure performs well in finite samples, and the empirical analysis not only supports the existence of regime-switching in the quantile autoregression model, but also has a good performance on data fitting. [ABSTRACT FROM AUTHOR]

The simple linear regression model and the associated goodness-of-fit measure, the coefficient of determination, R2, are only appropriate when all measurement errors are associated with the measurement of the data in the dependent variable. When measurement errors are assumed in both variables, a Deming regression can be used; however, there is no associated R2-type measure for this specific type of regression. In this paper, we propose a measure, R g 2 which utilizes the minimum percentage improvement of the Deming regression over either the horizontal or the vertical line through the centroid of the data. We investigate some properties of this measure and its relation to R2. We also consider other candidate methodologies for a generalized R2 measure for a Deming regression model and investigate strengths and weaknesses of each as a way of beginning the conversation about which measure is the best and for which applications it is most suited. [ABSTRACT FROM AUTHOR]

The common parameter estimation methods of panel data linear model include least square dummy variable estimation, two-stage least square estimation, quasi-maximum likelihood estimation and generalized moment estimation. However, these estimation methods are not robust and are easily affected by outliers. Firstly, this paper extends support vector regression algorithm to fit several parallel super-plane simultaneously and provide a novel robust estimation of fixed-effect panel data linear model; then using the kernel trick, a robust estimation for fixed effect panel data nonlinear model is introduced. Finally, the proposed model (linear or nonlinear) is applied in forecasting air quality index of the cities of Jing-Jin-Ji district in China. Experiments shows that our proposed model are robust and have good generalization performance. [ABSTRACT FROM AUTHOR]

As a basic model, an uncertain regression model with autoregressive time series errors has been investigated. This paper proposes another fundamental model—uncertain regression model with moving average time series errors—by assuming that the errors of regression model have a moving average structure. Then the principle of least squares is used to estimate the unknown parameters in the model. Based on the fitted model, the forecast value and confidence interval of the future data are derived. Finally, an example is presented to verify the feasibility of this approach. [ABSTRACT FROM AUTHOR]

It is well known that the variances of the least squares estimates are large and they can be far away from their true values in the case of multicollinearity. Therefore, the ridge regression method can be used as an alternative to the least squares method. However, the ridge estimator has a disadvantage that its distribution is unknown, so only asymptotic confidence intervals are obtained. The purpose of this paper is to study the impact of several ridge regularization parameters on the mean interval lengths of the confidence intervals and coverage probabilities constructed by the ridge estimator. A bootstrap method for the selection of ridge regularization parameter is used as well as the parametric methods. In order to compare the confidence intervals, standard normal approximation, student-t approximation and bootstrap methods are used and comparison is illustrated via real data and simulation study. The simulation study shows that the bootstrap choice of ridge regularization parameter yields narrower standard normal approximated confidence intervals than the PRESS choice of ridge regularization parameter but wider standard normal approximated, student-t approximated and bootstrap confidence intervals than the GCV choice of ridge regularization parameter. [ABSTRACT FROM AUTHOR]

Empirical likelihood has been widely used in survival data analysis recently. In this paper, we combine Bayesian idea with empirical likelihood and develop a Bayesian empirical likelihood method to analyze current status data based on the linear regression model. By constructing unbiased transformation of current status data, we derive an empirical log-likelihood function. The normal prior distribution and a Metro-Hastings method are presented to make Bayesian posterior inference. The theoretical properties of the estimators are proposed. Extensive simulation studies indicate that Bayesian empirical likelihood method performs much better than the empirical likelihood method in terms of coverage probability. Finally, we apply two real data to illustrate the proposed method. [ABSTRACT FROM AUTHOR]

This paper presents a statistical tool of uncertain significance test that uses uncertainty theory to test whether certain prespecified regression coefficients can be regarded as zero. A numerical example is given to illustrate how to test the significance of regression coefficients in an uncertain regression model. In order to compare uncertain significance test with stochastic significance test, both of these significance testing approaches are applied in studying the relationship between GDP and four indicators, including urban population scale, volume of foreign trade, fiscal expenditure, and water resource. The results show that uncertain significance test is more appropriate than stochastic significance test. [ABSTRACT FROM AUTHOR]

The length-biased Birnbaum-Saunders distribution is both useful and practical for environmental sciences. In this paper, we initially derive some new properties for the length-biased Birnbaum-Saunders distribution, showing that one of its parameters is the mode and that it is bimodal. We then introduce a new regression model based on this distribution. We implement the maximum likelihood method for parameter estimation, approach interval estimation and consider three types of residuals. An elaborate Monte Carlo study is carried out for evaluating the performance of the likelihood-based estimates, the confidence intervals and the empirical distribution of the residuals. Finally, we illustrate the proposed regression model with the use of a real meteorological data set. [ABSTRACT FROM AUTHOR]

Besides censoring, multicollinearity and outliers are two common problem in regression analysis. In this paper we propose a family of robust ridge estimators for the censored semiparametric regression models. The proposed robust estimators is based on least trimmed squares (LTS) method. This method is insensitive to corruption due to outliers, provided that the outliers constitute less than 50 % of the set, in other words, LTS is a robust estimator with a 50 % breakdown point. The FAST-LTS algorithm is developed for the computation of the estimators. Furthermore, a robust method for the estimate of shrinkage parameters is suggested. Monté-Carlo simulation study demonstrates the merit of the new method in the aspect of solving the multicollinearity and sensitivity to outliers over the ordinary least squares estimation. Finally, an example of real data is given for illustration. [ABSTRACT FROM AUTHOR]

The estimation of the slope parameter of a simple linear regression model in the presence of nonsample prior information under the reflected normal loss function is considered. Usually, the traditional estimation methods such as the least squared (LS) error are used to estimate the slope parameter. Sometimes the researcher has information about the unknown slope parameter from experience as a point guess, the nonsample prior information. In this paper, the shrinkage pretest estimators are introduced and their risk functions are derived under the reflected normal loss function. Several methods of finding distrust coefficient of the shrinkage pretest estimators are proposed. The behavior of the estimators are compared using a simulation study. The results show that the shrinkage pretest estimator outperforms the LS estimator when nonsample prior information is close to the real value. A real data set is analyzed for illustrating the results. [ABSTRACT FROM AUTHOR]

The observations of some samples are usually collected in an imprecise way. By employing uncertain variables to model these imprecise observations, this paper proposes uncertain statistical inferences for nonparametric regression model based on the least absolute deviations criterion. A numerical example and simulation comparison with least squares estimate are presented to illustrate the proposed method. [ABSTRACT FROM AUTHOR]

Linear regression models which account for skewed error distributions with fat tails have been previously studied. These two important features, skewness, and fat tails, are often observed in real data analyses. Covariates measured with an error also happen frequently in the observational data set-up. As a motivating example, wind speed as a covariate is usually used, among other covariates, to estimate the particulate matter (PM) which is one of the most critical air pollutants and has a major impact on human health and on the environment. However, the wind speed is measured with error and the distribution of PM is neither symmetric nor normally distributed (see Section "PM data application in Canada" for more details). Ignoring the issue of measurement error in covariates may produce bias in model parameters estimate and lead to wrong conclusions. In this paper, we propose an approach to study properly linear regression models where the covariates are measured with error and the error distribution is skewed with fat tails. We use a hierarchical Bayesian approach for inference, addressing also sensitivity of the results to priors. Performance of the proposed approach is evaluated through a simulation study and also by a real data application (PM in Canada). [ABSTRACT FROM AUTHOR]

Interval-censored failure time data often occur in medical follow-up studies among other areas. Regression analysis of linear transformation models with interval-censored data has been investigated by several authors under different contexts, but most of the existing methods assume that the covariates are discrete because these methods rely on the estimation of conditional survival distribution function. Without this assumption, this paper constructs a new generalized estimating equation using the propensity score. The proposed inference procedure does not need to estimate the conditional survival distribution any more and then can be used not only in the discrete but also in the continuous covariate situation. The asymptotic properties of the resulting estimates are given, and an extensive simulation study is performed. Finally, the application to two real datasets is also provided. Key words: Estimating equation; Interval-censored data; Propensity score; Linear transformation model. [ABSTRACT FROM AUTHOR]

This paper is concerned with the consistency of nonparametric regression model. For the weighted estimator of unknown regression function, the strong consistency, the complete consistency and the convergence rate of the complete consistency are investigated under some mild conditions. These results extend or improve the corresponding ones of Yang et al. (2018) for extended negatively dependent (END, for short) random variables to asymptotically almost negatively associated random variables. Also, the simulation study of the finite samples provided in this paper shows the validity of our results. [ABSTRACT FROM AUTHOR]

The case-cohort design is used in large cohort study to improve the efficiency and reduce the cost. In modeling process, we meet the situation that some covariates in a regression model are distorted by an unknown function of an observable confounding variable in a multiplicative form. In this paper, we consider fitting covariate-adjusted proportional hazards model for case-cohort studies. We propose to estimate the distorted function by non parametrically regressing the observed covariates on the distorted confounder, and then an estimator for the regression parameter is obtained by using the estimated covariates. Under some mild assumptions, we establish the asymptotic properties of the proposed estimator. The results from both artificial and real data demonstrate good performance and practicality of the proposed method. [ABSTRACT FROM AUTHOR]

This paper considers the parameter estimation for the inverse Gaussian regression model (IGRM) in the presence of multicollinearity. The inverse Gaussian modified ridge-type estimator (IGMRTE) is developed for efficient parameter estimation and compared with other estimation methods such as the maximum likelihood estimator (MLE), ridge and Liu estimator. We derived the properties of the proposed estimator and conducted a theoretical comparison with some of the existing estimators using the matrix mean squared error and mean squared error criterions. Furthermore, the statistical properties of these estimators are systematically scrutinized via a Monte Carlo simulation study under different conditions. The findings of the simulation study demonstrate that the proposed IGMRTE showed a much more robust behavior in the presence of severe multicollinearity. A real life example is also analyzed to evaluate the effectiveness of the estimators under study. Both the simulation and the application results confirm the use of IGMRTE for the estimation of unknown regression coefficients of the IGRM when the explanatory variables are highly correlated. [ABSTRACT FROM AUTHOR]

In our research work, the problem of how to construct the optimal design of collapse mixture model has been further explored and studied, and some new progress has been made. In this paper an abstract optimal criterion which is called normality optimality criteria is proposed by specifying some features of its equivalent matrix and invariant. And the optimality criteria, such as D-, A-, and R- etc., are proved to be normality optimality criteria. Meanwhile, the concept of collapsed homogeneous linear model is also proposed, and an inequality related to the collapsed homogeneous linear model is also proved. For multi mixture experiment, a concept of optimal weights for collapsed mixture model is also proposed first. For the so-called normality optimality criterion, an optimal weight for the collapsed homogeneous linear model is obtained by using these concepts and inequality mentioned above. The results obtained in this paper are not only applicable to the optimality criteria, such as D-, A-, and R- etc., but also applicable to the normal optimality criteria satisfying certain conditions. [ABSTRACT FROM AUTHOR]

Grouped and right-censored (GRC) count data are widely adopted to study some sensitive topics or to collect information from less cognitive respondents in many research fields, such as psychology, sociology, and criminology. However, theoretical analysis of GRC counts is involved due to the co-existence of grouping schemes and right-censoring schemes. Recently, a modified Poisson regression model has been proposed to analyze GRC count data under the framework of maximum likelihood estimation. In this paper, I study the asymptotic properties of the maximum likelihood estimators of GRC counts that can cover the modified Poisson estimator. Existing results on modified Poisson estimators for GRC counts are only applicable to stochastic regressors with strictly positive definite Fisher information matrices. Results in this paper are derived under a milder condition that the information matrix of observations is divergent, which can cover the results for the stochastic case in the almost sure sense. Real data simulations are provided to investigate drug use in America. [ABSTRACT FROM AUTHOR]

Samples often are collected by a network in many modern applications, and the network structure information is potentially helpful in making regression predictions. However, most regression models assume the samples are independent, such as Lasso. Motivated by this, taking the network information into account, we propose a Network Lasso model for regression prediction in this paper. Specially, we consider the effect of the neighborhoods to each response and model each yi as a linear combination of the covariates xi, the connected neighbors yj, and an error term ϵi. The corresponding coefficients are referred to effect of node and neighborhoods, respectively. The consistency of the estimators are also established under the regimes where the neighborhoods effect coefficients are known and unknown, respectively. Finally, we evaluate the performance of the proposed model through a series of simulations and a latitude data example. [ABSTRACT FROM AUTHOR]

Estimation and prediction of regression models with partition forms are widely applied techniques in statistical inference and data analysis. In this paper, we consider some fundamental inference problems regarding a linear random-effects model (LREM) and its reduced models without statistical distribution assumptions for error terms. We shall present a partition form of LREM and its correctly-reduced models, introduce the consistency concepts of the LREM and its reduced models, define the predictability/estimability of unknown parameters in the LREM and its reduced models, establish the matrix equations and analytical formulas associated with best linear unbiased predictors (BLUPs) and best linear unbiased estimators (BLUEs) of all unknown parameter vectors in the LREM and its reduced models, and present many fundamental decomposition equalities for the BLUPs/BLUEs of all unknown parameters in the LREM and its reduced models. [ABSTRACT FROM AUTHOR]

In this paper, we propose a nonconcave penalized M-estimation of the least absolute relative errors (penalized M-LARE) method for a sparse multiplicative regression model, where the dimension of model can increase with the sample size. Under certain appropriate conditions, the consistency and asymptotic normality for the penalized M-LARE estimator are established. Simulations and a real data analysis are in support of our theoretical results and illustrate that the proposed method performs well. [ABSTRACT FROM AUTHOR]

In this paper, we study the consistency of the P–C estimator in non parametric regression model based on m-END errors, and obtain the convergence rates of the complete consistency by using the inequalities for m-END sequence. Finally, some simulations are illustrated. [ABSTRACT FROM AUTHOR]

In this paper, we make use of meta-elliptical copula functions to build a new multivariate distribution with fixed marginal distributions and dependence structure to analyze bounded data. Specifically, we present a flexible p-elliptical multivariate probability distribution in the hypercube (0 , 1) p p with fixed marginal GF-quantile distributions. We then present some illustrative examples and a meta-elliptical multivariate regression model as a flexible alternative to the multivariate normal regression model on unit intervals. A simulation study and real-life data analysis using a Bayesian framework with the extreme-value quantile functions show the flexibility of the proposed meta-multivariate normal regression model for modeling the observed proportion response variables. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a robust estimator of the tail index of a Pareto-type distribution. The estimator is obtained through the use of the minimum density power divergence with an exponential regression model for log-spacings of top order statistics. The proposed estimator is compared to existing minimum density power divergence estimators of the tail index based on fitting an extended Pareto distribution and exponential regression model on log-ratio of spacings of order statistics. We derive the influence function and gross error sensitivity of the proposed estimator of the tail index to study its robustness properties. In addition, a simulation study is conducted to assess the performance of the estimators under different contaminated samples from different distributions. The results show that our proposed estimator of the tail index has better mean square errors and is less sensitive to an increase in the number of top order statistics. In addition, the estimation of the exponential regression model yields estimates of second-order parameters that can be used for estimation of extreme events such as quantiles and exceedance probabilities. The proposed estimator is illustrated with practical datasets on insurance claims and calcium content in soil samples. [ABSTRACT FROM AUTHOR]

This paper deals with the issue of testing hypotheses in the censored exponential regression model in small and moderate-sized samples. We focus on four tests, namely the Wald, likelihood ratio, score, and gradient tests. These tests rely on asymptotic results and are unreliable when the sample size is not large enough to guarantee a good agreement between the exact distribution of the test statistic under a null hypothesis and the corresponding reference chi-squared asymptotic distribution. Bartlett and Bartlett-type corrections typically attenuate the size distortion of the tests. These corrections are available in the literature for the likelihood ratio and score tests in the class of censored exponential regression models. A Bartlett-type correction for the gradient test is derived in this paper in this class of models. Additionally, we also propose bootstrap-based inferential improvements to the four tests mentioned. We numerically compare the tests through extensive Monte Carlo simulation experiments. The numerical results reveal that the corrected and bootstrapped tests exhibit type I error probability closer to the chosen nominal level with virtually no power loss. We also present an empirical application for illustrative purposes. [ABSTRACT FROM AUTHOR]

In a usual meta analysis of regression, it is assumed that co-variance among studies are zero. However, the main utility of a meta analysis is to provide an estimated overall effect by combining the results from related small studies. Therefore, incorporating co-variance among those small studies is essential, and in our earlier work, it was shown to improve the estimates obtained from the proposed generalized least square approach. In this paper, we provide a review of meta analysis of regression, then present an improved weighed least square approach to meta analysis that takes account into an appropriate co-variance structure among related studies. We illustrate our proposed method in a linear-circular regression setting with application to forecasting problem in Environmental Sciences, and compare the different approaches presented in this paper using the mean square prediction error (MSPE). [ABSTRACT FROM AUTHOR]

In this paper, we propose a new method to compare two or more panel data regression models. We aim to propose a method that is easily applicable to test the hypothesis of equality of regression coefficient vectors in panel data models with one-way and two-way error component regression. We present the results of our simulation study to compare our parametric bootstrap method with the other methods. [ABSTRACT FROM AUTHOR]

Based on the approach of left and right kernel smoothing with unilateral kernel function, we, in this paper, define estimators of change point and jump size in nonparametric regression model with response missing at random. It is shown that the change point estimator is n-consistent and converges to the smallest maximizer of one-dimensional bilateral compound Poisson process, the jump size estimator is asymptotically normal. A simulation study is conducted to investigate the finite sample behavior for the proposed methods. [ABSTRACT FROM AUTHOR]

Zero-inflated models have become a popular tool for assessing relationships between explanatory variables and a zero-inflated count outcome. In these models, regression coefficients have latent class interpretations, where latent classes correspond to a susceptible subpopulation with observations generated from a count distribution and a non susceptible subpopulation that provides only zeros. However, it is often of interest to evaluate covariates effects in the overall mixture population, that is, on the marginal mean of the zero-inflated count. Marginal zero-inflated models, such as the marginal zero-inflated Poisson models, have been developed for that purpose. They specify independent submodels for the susceptibility probability and the marginal mean of the count response. When the count outcome is bounded, it is tempting to formulate a marginal zero-inflated binomial model in the same fashion. This, however, is not possible, due to inherent constraints that relate, in the zero-inflated binomial model, the susceptibility probability and the latent and marginal means of the count outcome. In this paper, we propose a new marginal zero-inflated binomial regression model that accommodates these constraints. We investigate the maximum likelihood estimator in this model, both theoretically and by simulations. An application to the analysis of health-care demand is provided for illustration. [ABSTRACT FROM AUTHOR]

This paper studies projection pursuit emulation for computer experiments with many input variables. This method aims at capturing the most influential directions of the inputs to the response, and thus the active dimensionality is reduced. Its interpolation property is proved under certain conditions. We also propose a two-stage method to handle the case where the projection pursuit method does not converge. Simulation studies show that the proposed methods are more efficient than the traditional Kriging methods. [ABSTRACT FROM AUTHOR]

In this paper, we propose a penalized estimation method for finite mixture of ultra-high dimensional regression models. A two-step procedure is explored. Firstly, we conduct order selection with the number of components unknown. Then variable selection is applied to ultra-high dimensional regression models. A specific EM algorithm is designed to maximize penalized log-likelihood function. We demonstrate our method by numerical simulations which performs well. Further, an empirical study of return on equity (ROE) prediction is shown to consolidate our methodology. [ABSTRACT FROM AUTHOR]

Missing data is a common problem in general applied studies, and specially in clinical trials. For implementing sensitivity analysis, several multiple imputation methods exist, like sequential imputation, which restricts to monotone missingness, and Bayesian, where the imputation and analysis models differ, entailing overestimation of variance. Also, full conditional specification provides a conditional interpretation of sensitivity parameters, requiring further calibration to get the desired marginal interpretation. We propose in this paper a multiple imputation procedure, based on a multivariate linear regression model, which keeps compatibility in sensitivity analysis under intermittent missingness, providing a marginal interpretation of the elicited parameters. Simulation studies show that the method behaves well with longitudinal data and remains robust under demanding constraints. We conclude the possibility of situations not covered by the existing methods and well suited for our proposal, which allows more efficient handling of a given multivariate linear regression structure. Its use is illustrated in a real case study, where a sensitivity analysis is accomplished. [ABSTRACT FROM AUTHOR]

In classical linear regression analysis problems, the ordinary least-squares (OLS) estimation is the popular method to obtain the regression weights, given the essential assumptions are satisfied. However, often, in real-life studies, the response data and its associated explanatory variables do not meet the required conditions, in particular under multicollinearity, and hence results can be misleading. To overcome such problem, this paper introduces a novel generalized difference-based weighted mixed almost unbiased Liu estimator. The performance of this new estimator is evaluated against the classical estimators using the mean squared error. This is followed by an approach to select the Liu parameter and in this context, a non-stochastic weight is also considered. Monte Carlo simulation experiments are executed to assess the performance of the new estimator and subsequently,we illustrate its application to a real-life data example. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of the nonparametric analysis by the relative-error regression when the explanatory of a variable is of infinite dimension. Based on k-Nearest Neighbors procedure (kNN), we construct an estimator and establish its asymptotic properties. Precisely, we show its Uniform consistency in Number of Neighbors (UNN) with the precision of the convergence rate. Some empirical studies are also performed to highlight the impact of this asymptotic result in nonparametric functional statistics. [ABSTRACT FROM AUTHOR]

In this paper, we study the complete moment convergence for arrays of rowwise m-extended negatively dependent (m-END) random variables, which generalizes some corresponding ones for complete convergence. We also give an application to non-parametric regression model based on m-END errors by using the complete convergence that we establish. Finally, the choice of the fixed design points and the weight functions for the nearest neighbor estimator are proposed. We also provide a numerical simulation to verify the validity of our theoretical result. [ABSTRACT FROM AUTHOR]

Medical costs are often skewed to the right, heteroscedastic, and having a sophisticated relation with covariates. Moreover, medical cost datasets are always massive, such as in the New York Statewide Planning and Research Cooperative System Expenditure Study. Different observations can depend on each other as the spatial distribution of diseases induces complex correlation among patients coming from nearby communities. Therefore, it is not enough if only focus on the mean function regression models with low-dimensional covariates, small sample size and identically independent observations. In this paper, we propose a new quantile regression model to analyze medical costs. A network term is introduced to account for the dependence among different observations. We also consider variable selection for massive datasets. An adaptive lasso penalized variable selection method is applied in a parallel manner, the resulting estimators are combined through minimizing an extra penalized loss function. Simulation studies are conducted to illustrate the performance of the estimation method. We apply our method to the analysis of the New York State's Statewide Planning and Research Cooperative System, 2013. [ABSTRACT FROM AUTHOR]

In this paper, we propose an outlier-detection approach that uses the properties of an intercept estimator in a difference-based regression model (DBRM) that we first introduce. This DBRM uses multiple linear regression, and invented it to detect outliers in a multiple linear regression. Our outlier-detection approach uses only the intercept; it does not require estimates for the other parameters in the DBRM. In this paper, we first employed a difference-based intercept estimator to study the outlier-detection problem in a multiple regression model. We compared our approach with several existing methods in a simulation study and the results suggest that our approach outperformed the others. We also demonstrated the advantage of our approach using a real data application. Our approach can extend to nonparametric regression models for outliers detection. [ABSTRACT FROM AUTHOR]

A correction to the article "A Note on Directional Dependence in Regression Setting," by Engin A. Sungur that was published in a previous issue is presented.