High-dimensional posterior consistency of the Bayesian lasso

ABSTRACT

This paper considers posterior consistency in the context of high-dimensional variable selection using the Bayesian lasso algorithm. In a frequentist setting, consistency is perhaps the most basic property that we expect any reasonable estimator to achieve. However, in a Bayesian setting, consistency is often ignored or taken for granted, especially in more complex hierarchical Bayesian models. In this paper, we have derived sufficient conditions for posterior consistency in the Bayesian lasso model with the orthogonal design, where the number of parameters grows with the sample size.     

Some theoretical results concerning non parametric estimation by using a judgment poststratification sample

ABSTRACT

In this paper, some of the properties of non parametric estimation of the expectation of g(X) (any function of X), by using a judgment poststratification sample (JPS), have been discussed. A class of estimators (including the standard JPS estimator and a JPS estimator proposed by Frey and Feeman (2012 Frey, J., Feeman, T.G. (2012). An improved mean estimator for judgment post-stratification. Comput. Stat. Data Anal. 56(2):418–426.[Crossref], [Web of Science ®] , [Google Scholar], Comput. Stat. Data An.) is considered. The paper provides mean and variance of the members of this class, and examines their consistency and asymptotic distribution. Specifically, the results are for the estimation of population mean, population variance, and cumulative distribution function. We show that any estimators of the class may be less efficient than simple random sampling (SRS) estimator for small sample sizes. We prove that the relative efficiency of some estimators in the class with respect to balanced ranked set sampling (BRSS) estimator tends to 1 as the sample size goes to infinity. Furthermore, the standard JPS mean estimator, and Frey–Feeman JPS mean estimator are specifically studied and we show that two estimators have the same asymptotic distribution. For the standard JPS mean estimator, in perfect ranking situations, optimum values of H (the ranking class size), for different sample sizes, are determined non parametrically for populations that are not heavily skewed or thick tailed.     

A decision-theoretic approach to variable selection in discriminant analysis

In discriminant analysis it is often desirable to find a small subset of the variables that were measured on the individuals of known origin, to be used for classifying individuals of unknown origin. In this paper a Bayesian approach to variable selection is used that includes an additional subset of variables for future classification if the additional measurement costs for this subsst are lower than the resulting reduction in expected misclassification costs.     

Approximate regression models and splines

The literature pertaining to splines in regression analysis is reviewed. Spline regression is motivated as a simple extension of the basic polynomial regression model. Using this framework, the concepts of fixed and variable knot spline regression are developed and corresponding inferential procedures are considered. Smoothing splines are also seen to be an extension of polynomial regression and various optimality properties, as well as inferential and diagnostic methods, for these types of splines are discussed.     

On the construction of hypercubic design

Hypercubic design was introduced by Shah (1958) and Kusumoto(1965) in which the t=v^m treatments are represented by n-plets (x₁, x₂, ..., x_m),where 1≤ x₁, x₂, ..., x_m ≤v, and two treatments are said to be i-th associates if they differ in exactly i components. This paper deals with the construction of some hypercubic designs and gives their application to confounding plans for symmetrical factorial experiments. The proposed methods prove to be quite flexible in terms of choice of possible block sizes and are easy to use.     

Teaching control and capability at alcoa

The past efforts by the Aluminum Company of America (Alcoa) to create a statistically capable work force have met with limited success. Faced with a mixed record of translating statistical training to on-the-job application and meeting demanding executive expectations, members of the Alcoa Quality, Training and Education Department are creating tools which help Alcoa develop quantitatively literate employees- One result is a workshop which gives the participants hands-on experience and provides them with an appropriate set of statistical tools “just-in time”. This paper outlines the elements of the workshop, emphasizing that bringing a process into control and making it capable is really empirical learning. Learning models are explored, and an algorithm outlining a methodology to bring processes into control and make them capable is presented.     

Local Linear GMM Estimation of Functional Coefficient IV Models With an Application to Estimating the Rate of Return to Schooling

We consider the local linear generalized method of moment (GMM) estimation of functional coefficient models with a mix of discrete and continuous data and in the presence of endogenous regressors. We establish the asymptotic normality of the estimator and derive the optimal instrumental variable that minimizes the asymptotic variance-covariance matrix among the class of all local linear GMM estimators. Data-dependent bandwidth sequences are also allowed for. We propose a nonparametric test for the constancy of the functional coefficients, study its asymptotic properties under the null hypothesis as well as a sequence of local alternatives and global alternatives, and propose a bootstrap version for it. Simulations are conducted to evaluate both the estimator and test. Applications to the 1985 Australian Longitudinal Survey data indicate a clear rejection of the null hypothesis of the constant rate of return to education, and that the returns to education obtained in earlier studies tend to be overestimated for all the work experience.     

Discrete-time GIX/Geo/1/N queue with negative customers and multiple working vacations

Using the supplementary variable and the embedded Markov chain method, we consider a discrete-time batch arrival finite capacity queue with negative customers and working vacations, where the RCH killing policy and partial batch rejection policy are adopted. We obtain steady-state system length distributions at pre-arrival, arbitrary and outside observer’s observation epochs. Furthermore, we consider the influence of system parameters on several performance measures to demonstrate the correctness of the theoretical analysis.     

若干可积的二维变系数线性微分系统

本文谈二维变系数线性微分系统的若干可积类,且指出求它们的通解的具体步骤。     

我国农民生育行为的社会结构解释

通过分析“成本-效用”的经济因素及文化因素解释说,对于农民非要生育男孩这一生育行为的解释在理论与方法论方面存在的局限性,提出了使用社会结构的分析视角来理清各影响因素彼此间的关系,即从内生变量因素(农村家庭养老、家庭结构和社区结构)以及外生变量因素(户籍制度、计划生育政策)2个方面对农民偏好男孩这一生育行为作出分析和解释。最终认为,理解并认可农民想要一个男孩是一件并不过分的事,这有助于促进人口工作取得实际成效。