Bayesian Conditional Mean Estimation in Log‐Normal Linear Regression Models with Finite Quadratic Expected Loss

Log‐normal linear regression models are popular in many fields of research. Bayesian estimation of the conditional mean of the dependent variable is problematic as many choices of the prior for the variance (on the log‐scale) lead to posterior distributions with no finite moments. We propose a generalized inverse Gaussian prior for this variance and derive the conditions on the prior parameters that yield posterior distributions of the conditional mean of the dependent variable with finite moments up to a pre‐specified order. The conditions depend on one of the three parameters of the suggested prior; the other two have an influence on inferences for small and medium sample sizes. A second goal of this paper is to discuss how to choose these parameters according to different criteria including the optimization of frequentist properties of posterior means.     

Dealing with the Initial Observation in the LM Unit Root Test

This article proposes a linearly weighted unit root test with a new weighting scheme which reflects the trade-off in power between the ADF and LM tests regarding the initial value of a time series. Simulation results indicate that the proposed test has better power performance and works better than other available tests in the literature for a range of initial conditions.     

Influence diagnostics for the Weibull-Negative-Binomial regression model with cure rate under latent failure causes

In this paper, we propose a flexible cure rate survival model by assuming that the number of competing causes of the event of interest follows the Negative Binomial distribution and the time to event follows a Weibull distribution. Indeed, we introduce the Weibull-Negative-Binomial (WNB) distribution, which can be used in order to model survival data when the hazard rate function is increasing, decreasing and some non-monotonous shaped. Another advantage of the proposed model is that it has some distributions commonly used in lifetime analysis as particular cases. Moreover, the proposed model includes as special cases some of the well-know cure rate models discussed in the literature. We consider a frequentist analysis for parameter estimation of a WNB model with cure rate. Then, we derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes and present some ways to perform global influence analysis. Finally, the methodology is illustrated on a medical data.     

Bayesian variable selection approach to a Bernstein polynomial regression model with stochastic constraints

This paper provides a Bayesian estimation procedure for monotone regression models incorporating the monotone trend constraint subject to uncertainty. For monotone regression modeling with stochastic restrictions, we propose a Bayesian Bernstein polynomial regression model using two-stage hierarchical prior distributions based on a family of rectangle-screened multivariate Gaussian distributions extended from the work of Gurtis and Ghosh [7 S.M. Curtis and S.K. Ghosh, A variable selection approach to monotonic regression with Bernstein polynomials, J. Appl. Stat. 38 (2011), pp. 961–976. doi: 10.1080/02664761003692423[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]]. This approach reflects the uncertainty about the prior constraint, and thus proposes a regression model subject to monotone restriction with uncertainty. Based on the proposed model, we derive the posterior distributions for unknown parameters and present numerical schemes to generate posterior samples. We show the empirical performance of the proposed model based on synthetic data and real data applications and compare the performance to the Bernstein polynomial regression model of Curtis and Ghosh [7 S.M. Curtis and S.K. Ghosh, A variable selection approach to monotonic regression with Bernstein polynomials, J. Appl. Stat. 38 (2011), pp. 961–976. doi: 10.1080/02664761003692423[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]] for the shape restriction with certainty. We illustrate the effectiveness of our proposed method that incorporates the uncertainty of the monotone trend and automatically adapts the regression function to the monotonicity, through empirical analysis with synthetic data and real data applications.     

扶贫政策的负外部性及其化解

在脱贫攻坚中,对重点贫困地区的精确瞄准与偏向投入,在一定程度上对非贫困县、非贫困村与非贫困户产生了必然的政策负外部性,表现为县域脱贫结构失衡、村庄帮扶悬崖效应与边缘人群争贫风险。究其原由,在公共政策过程中,竞争性的政策汲取、排他性的政策分配与分割性的政策评价是负外部性的三种发生机理。为此需要建立上下融合减贫机制,探索社区主导发展模式,拓展村民赋权参与空间,通过政策纠正、调适以消解和弥补政策负效应,强化政治决策与分配的正义性。     

Quasi-binomial zero-inflated regression model suitable for variables with bounded support

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.     

A new heavy-tailed distribution defined on the bounded interval: the logit slash distribution and its application

This paper proposes a new heavy-tailed and alternative slash type distribution on a bounded interval via a relation of a slash random variable with respect to the standard logistic function to model the real data set with skewed and high kurtosis which includes the outlier observation. Some basic statistical properties of the newly defined distribution are studied. We derive the maximum likelihood, least-square, and weighted least-square estimations of its parameters. We assess the performance of the estimators of these estimation methods by the simulation study. Moreover, an application to real data demonstrates that the proposed distribution can provide a better fit than well-known bounded distributions in the literature when the skewed data set with high kurtosis contains the outlier observations.     

Inference on a progressive type I interval-censored truncated normal distribution

In this paper, we consider the problem of making statistical inference for a truncated normal distribution under progressive type I interval censoring. We obtain maximum likelihood estimators of unknown parameters using the expectation-maximization algorithm and in sequel, we also compute corresponding midpoint estimates of parameters. Estimation based on the probability plot method is also considered. Asymptotic confidence intervals of unknown parameters are constructed based on the observed Fisher information matrix. We obtain Bayes estimators of parameters with respect to informative and non-informative prior distributions under squared error and linex loss functions. We compute these estimates using the importance sampling procedure. The highest posterior density intervals of unknown parameters are constructed as well. We present a Monte Carlo simulation study to compare the performance of proposed point and interval estimators. Analysis of a real data set is also performed for illustration purposes. Finally, inspection times and optimal censoring plans based on the expected Fisher information matrix are discussed.     

Statistical inference based on generalized Lindley record values

This paper addresses the problems of frequentist and Bayesian estimation for the unknown parameters of generalized Lindley distribution based on lower record values. We first derive the exact explicit expressions for the single and product moments of lower record values, and then use these results to compute the means, variances and covariance between two lower record values. We next obtain the maximum likelihood estimators and associated asymptotic confidence intervals. Furthermore, we obtain Bayes estimators under the assumption of gamma priors on both the shape and the scale parameters of the generalized Lindley distribution, and associated the highest posterior density interval estimates. The Bayesian estimation is studied with respect to both symmetric (squared error) and asymmetric (linear-exponential (LINEX)) loss functions. Finally, we compute Bayesian predictive estimates and predictive interval estimates for the future record values. To illustrate the findings, one real data set is analyzed, and Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation and prediction.