Thinning operation is a stochastic operation that shrinks a random count variable into a smaller one. This kind of random operation has been intensively studied during the seventies to characterize some count distributions, such as the Poisson distribution using the binomial thinning operator (also named binomial damage model). Then, the closure under thinning operator has been studied in order to define some classes of integer valued autoregressive (INAR) models for count time series. These two properties will be studied in this paper for the new class of quasi Pólya thinning operators. Classical results concerning the binomial thinning operator are recovered as a special case. The quasi Pólya thinning operator is related to the new class of quasi Pólya splitting distributions, defined for multivariate count data. The probabilistic graphical model (PGM) of these multivariate distributions is characterized. Finally a general class of integer valued autoregressive models is introduced, including the usual cases of Poisson marginal or generalized Poisson as a special cases and the generalized negative binomial as a new case.

In this paper, we consider the estimation and variable selection problem for partially linear additive spatial autoregressive models (PLASARM). We propose a robust estimation of two-stage Walsh-average regression (2SWAR) based on Walsh-average regression and instrumental variable method. Under some mild conditions, we obtain and theoretically prove the asymptotic normality of finite parameter vectors and the convergence rate of the nonparametric part. In addition, We also propose a robust variable selection method and further demonstrate its ability to consistently identify real models. We further carry out Monte Carlo simulation and real data analysis, both of which yield promising numerical results.

Experiments with repeated measures are the ones where more than one observation per subject is available. To model of such experiments, dependency within subjects needs to be taken into consideration. In cases where the variable of interest is bounded in $(\mathit{a},\mathit{b})$ with $\mathit{a}<\mathit{b}$ known reals, there are few proposals to model correlated bounded data most part being based on Beta, Simplex and Unit gamma distributions. In particular, for marginal modeling of the mean and precision/dispersion, Simplex and Beta models based on Generalized Estimating Equations (GEE) are used. In this paper, to take account of possible within-subject dependence using the GEE approach, we proposed an Unit Gamma regression model used to modeling bounded data in a unit interval. In this paper, we developed residuals and influence diagnostic tools to the Simplex and Unit Gamma models for correlated bounded data. Furthermore, To assess the finite-sample performance of the proposed estimators, we conducted a Monte Carlo simulation study. The methodology is illustrated with the analysis of a real data set. An $\mathtt{R}$ package was developed for all the new methodology described in this paper.

Divide-and-conquer methods for scalable Bayesian inference divide the massive data into subsets, sample from the subset posterior distributions, and then combine the results. We develop an asymptotically exact recombination method by matched samples. Subset posterior densities calculated by the Metropolis–Hastings samplers are recycled for evaluating the importance weight to reduce the computational burden. Our computationally efficient aggregation algorithm features a collection of consistent estimators of expectations with respect to the full posterior distribution. Weight degeneracy of the importance sampling is resolved by the matched-sample resample-move method, which handles heterogeneous and non-overlapping subposteriors. Numeric examples and real-world mortgage data applications demonstrate excellent performance of the novel approach.

This paper is concerned with sparse spatial panel data models under fixed effects and increasing dimensions of covariates. We develop a nonconcave selection approach for spatial effects recognition and covariates selection of the models. Theoretical results show that the proposed method has the oracle property in the sense that the estimators have consistency, sparsity and asymptotic normality under suitable conditions. Furthermore, we present an coordinate descent algorithm to deal with the nonlinearity that arises in the optimization procedure. Numerical experiments show that the recognition and selection procedure can be used to select important covariates, identify spatial effects and estimate unknown parameters simultaneously. At the same time, the benefits of the proposed method is assessed by comparing different analyses of real spatial penal data.

Multivariate count data with an excessive number of zeros occur commonly in practice. To deal with this kind of data, we introduce a simple and tractable parametric multivariate zero-inflated distribution, which corresponds to a multivariate extension of the univariate zero-inflated Bell–Touchard distribution. Various distributional properties are derived and, in particular, the marginal distributions are univariate zero-inflated Bell–Touchard distributions. The unknown parameters of the proposed multivariate zero-inflated distribution are estimated using the maximum likelihood estimation procedure. An empirical application that employs COVID-related real data is provided to illustrate the new multivariate zero-inflated distribution in practice, and comparison with some multivariate zero-inflated distributions is made.