Minimum average risk estimators for coefficients in linear models

We consider the problem of estimating the coefficient vector β of a linear regression model with quadratic loss function. Some biased estimators which utilize the prior information about β are considered. Also studied is the problem of estimating the parameters of an over-identified structural equation from undersized samples.     

An Empirical Study of Statistical Properties of Variance Partition Coefficients for Multi-Level Logistic Regression Models

Partitioning the variance of a response by design levels is challenging for binomial and other discrete outcomes. Goldstein (2003 Goldstein , H. ( 2003 ). Multilevel Statistical Models. 3rd ed . London : Edward Arnold . [Google Scholar]) proposed four definitions for variance partitioning coefficients (VPC) under a two-level logistic regression model. In this study, we explicitly derived formulae for multi-level logistic regression model and subsequently studied the distributional properties of the calculated VPCs. Using simulations and a vegetation dataset, we demonstrated associations between different VPC definitions, the importance of methods for estimating VPCs (by comparing VPC obtained using Laplace and penalized quasilikehood methods), and bivariate dependence between VPCs calculated at different levels. Such an empirical study lends an immediate support to wider applications of VPC in scientific data analysis.     

一类变系数边值问题的样条解法

本文讨论了一类三阶变系数微分方程的边值问题的样条解法．构造了一个四次样条的近似解,并证明了它的唯一性和收敛性．在文末举例说明本方法是可行的．     

Logistic模型的系数比较问题及解决策略：一个综述

本文介绍了Logistic模型中经常被忽视的系数比较问题,包括同一样本在不同模型间的系数比较和在不同样本或子群体间的模型系数比较。研究者往往会沿袭线性回归模型的系数比较方法,但这是不恰当的,因为Logistic模型存在未被观测到的异质性（残差变异）问题,所以模型间系数不能进行简单的直接比较。根据已有研究,本文总结了解决这一问题的五种策略,分别是“y*标准化”、KHB分解、异质选择模型、平均偏效应（APE）和线性概率模型（LPM）,然后利用CGSS2006数据,以教育递进率模型为例,比较这些解决策略的异同,最后总结这些策略的特征及适用情况。     

Inhomogeneous Markov Chains and Ergodicity Coefficients: John Hajnal (1924–2008)

In 1958, a paper by John Hajnal, a demographer and mathematical statistician, was fundamental in the revival of the theory of inhomogeneous Markov chains. Hajnal made his contribution by the development of tools for the analysis of weak ergodicity, and proofs of fundamental theorems. This article reviews Hajnal's career, and then focuses on the four topics: 1. ergodicity coefficients and the weak ergodicity theorem; 2. scrambling matrices; 3. the coupling theorem; and 4. non-negative matrix products. Related work by other authors, especially Wolfgang Doeblin, is mentioned in context. Attention is given to some recent surveys and applications of ergodicity coefficients, including the Google matrix.     

Bayes Hilbert Spaces

A Bayes linear space is a linear space of equivalence classes of proportional σ‐finite measures, including probability measures. Measures are identified with their density functions. Addition is given by Bayes' rule and substraction by Radon–Nikodym derivatives. The present contribution shows the subspace of square‐log‐integrable densities to be a Hilbert space, which can include probability and infinite measures, measures on the whole real line or discrete measures. It extends the ideas from the Hilbert space of densities on a finite support towards Hilbert spaces on general measure spaces. It is also a generalisation of the Euclidean structure of the simplex, the sample space of random compositions. In this framework, basic notions of mathematical statistics get a simple algebraic interpretation. A key tool is the centred‐log‐ratio transformation, a generalization of that used in compositional data analysis, which maps the Hilbert space of measures into a subspace of square‐integrable functions. As a consequence of this structure, distances between densities, orthonormal bases, and Fourier series representing measures become available. As an application, Fourier series of normal distributions and distances between them are derived, and an example related to grain size distributions is presented. The geometry of the sample space of random compositions, known as Aitchison geometry of the simplex, is obtained as a particular case of the Hilbert space when the measures have discrete and finite support.     

Selecting the regularization parameters in high-dimensional panel data models: Consistency and efficiency

This article considers panel data models in the presence of a large number of potential predictors and unobservable common factors. The model is estimated by the regularization method together with the principal components procedure. We propose a panel information criterion for selecting the regularization parameter and the number of common factors under a diverging number of predictors. Under the correct model specification, we show that the proposed criterion consistently identifies the true model. If the model is instead misspecified, the proposed criterion achieves asymptotically efficient model selection. Simulation results confirm these theoretical arguments.     

Bayesian inference for generalized additive mixed models based on Markov random field priors

Most regression problems in practice require flexible semiparametric forms of the predictor for modelling the dependence of responses on covariates. Moreover, it is often necessary to add random effects accounting for overdispersion caused by unobserved heterogeneity or for correlation in longitudinal or spatial data. We present a unified approach for Bayesian inference via Markov chain Monte Carlo simulation in generalized additive and semiparametric mixed models. Different types of covariates, such as the usual covariates with fixed effects, metrical covariates with non-linear effects, unstructured random effects, trend and seasonal components in longitudinal data and spatial covariates, are all treated within the same general framework by assigning appropriate Markov random field priors with different forms and degrees of smoothness. We applied the approach in several case-studies and consulting cases, showing that the methods are also computationally feasible in problems with many covariates and large data sets. In this paper, we choose two typical applications.