Non-negative estimation of variance components in heteroscedastic one-way random-effects ANOVA models

There is a considerable amount of literature dealing with inference about the parameters in a heteroscedastic one-way random-effects ANOVA model. In this paper, we primarily address the problem of improved quadratic estimation of the random-effect variance component. It turns out that such estimators with a smaller mean squared error compared with some standard unbiased quadratic estimators exist under quite general conditions. Improved estimators of the error variance components are also established.     

On approximate likelihood inference in a poisson mixed model

A two-step estimation approach is proposed for the fixed-effect parameters, random effects and their variance σ² of a Poisson mixed model. In the first step, it is proposed to construct a small σ²-based approximate likelihood function of the data and utilize this function to estimate the fixed-effect parameters and σ². In the second step, the random effects are estimated by minimizing their posterior mean squared error. Methods of Waclawiw and Liang (1993) based on so-called Stein-type estimating functions and of Breslow and Clayton (1993) based on penalized quasilikelihood are compared with the proposed likelihood method. The results of a simulation study on the performance of all three approaches are reported.     

中国古代审美观照的拓展与深化——论郭象“独化”哲学中的“俯仰”与“虚静”的整合

郭象独化哲学的崇有把自然山水审美引向独立,相当于掀起一场美学革命。这其中包括对俯仰与虚静两种审美观照的整合,深深影响了此后美学思想发展进程的基本走向。俯仰与虚静各有所长,亦各有所短。俯仰有观物取象之长,亦有思维的类比受限之短;虚静有排斥外通感物之短,亦有拓展心灵自由之长。郭象的无心玄应,唯感是从则构成二者的交融互补。其经无心过滤清洗过的唯感是从,一方面以俯仰的类比之短补入虚静的心灵自由之长,另一方面以隔绝外通之短补入俯仰的接物之长。中古山水审美的寓目辄书蔚然成风、巧言切状的追求及目击道存的观照方式的确认和推行,均得益于这种整合。它既是对庄子虚静排除具体感性的改造,又是对其目击道存理论依据的创造性发展,从而大大拓展和深化了中国古代的审美观照。     

Empirical nonparametric control charts for high-quality processes

For attribute data with (very) small failure rates often control charts are used which decide whether to stop or to continue each time r failures have occurred, for some r?1. Because of the small probabilities involved, such charts are very sensitive to estimation effects. This is true in particular if the underlying failure rate varies and hence the distributions involved are not geometric. Such a situation calls for a nonparametric approach, but this may require far more Phase I observations than are typically available in practice. In the present paper it is shown how this obstacle can be effectively overcome by looking not at the sum but rather at the maximum of each group of size r.     

描写充分与解释充分之张力：原则与参数框架的理论动因

通过总结Chomsky的＂句法理论中的原则与参数＂一文,回顾原则与参数框架产生的历史背景及其理论动因,梳理原则与参数框架的主要思想及内容,分析原则与参数框架提出的意义、它所面临的挑战及其发展前景。描写充分性与解释充分性之间的张力是原则与参数框架形成的理论动因。在生成语法追求＂超越解释的充分性＂这一更高目标的过程中,我们看到的是继续前进中的原则与参数。     

Variable selection for multivariate generalized linear models

Generalized linear models (GLMs) are widely studied to deal with complex response variables. For the analysis of categorical dependent variables with more than two response categories, multivariate GLMs are presented to build the relationship between this polytomous response and a set of regressors. Traditional variable selection approaches have been proposed for the multivariate GLM with a canonical link function when the number of parameters is fixed in the literature. However, in many model selection problems, the number of parameters may be large and grow with the sample size. In this paper, we present a new selection criterion to the model with a diverging number of parameters. Under suitable conditions, the criterion is shown to be model selection consistent. A simulation study and a real data analysis are conducted to support theoretical findings.     

Linear estimation for the extended exponential power distribution

Tiao and Lund [The use of OLUMV estimators in inference robustness studies of the location parameter of a class of symmetric distributions. J Amer Statist Assoc. 1970;65(329):370–386] tabulated the coefficients of the best linear unbiased estimators (BLUEs) of location and scale for a particular family of symmetric distributions. This family was a reparameterization of the extended exponential power distribution (EEPD) with the shape parameter restricted to be greater than or equal to one. In this work, we consider the BLU estimation of the location and scale parameters of the EEPD when the shape parameter is one-third and one-half. We obtain closed-form expressions for the single and product moments of the order statistics when the shape parameter is in general in the form of a reciprocal of an integer. These expressions are then used to determine the BLUEs and the corresponding variances for complete samples of size 20 and less. We consider some other linear estimators of the location and scale parameters and then compare them with the BLUEs. Finally, we present a numerical example to illustrate the developed results.     

Robust Priors in Nonlinear Panel Data Models

Many approaches to estimation of panel models are based on an average or integrated likelihood that assigns weights to different values of the individual effects. Fixed effects, random effects, and Bayesian approaches all fall into this category. We provide a characterization of the class of weights (or priors) that produce estimators that are first‐order unbiased. We show that such bias‐reducing weights will depend on the data in general unless an orthogonal reparameterization or an essentially equivalent condition is available. Two intuitively appealing weighting schemes are discussed. We argue that asymptotically valid confidence intervals can be read from the posterior distribution of the common parameters when N and T grow at the same rate. Next, we show that random effects estimators are not bias reducing in general and we discuss important exceptions. Moreover, the bias depends on the Kullback–Leibler distance between the population distribution of the effects and its best approximation in the random effects family. Finally, we show that, in general, standard random effects estimation of marginal effects is inconsistent for large T, whereas the posterior mean of the marginal effect is large‐T consistent, and we provide conditions for bias reduction. Some examples and Monte Carlo experiments illustrate the results.     

Decision Theory Applied to a Linear Panel Data Model

This paper applies some general concepts in decision theory to a linear panel data model. A simple version of the model is an autoregression with a separate intercept for each unit in the cross section, with errors that are independent and identically distributed with a normal distribution. There is a parameter of interest γ and a nuisance parameter τ, a N×K matrix, where N is the cross‐section sample size. The focus is on dealing with the incidental parameters problem created by a potentially high‐dimension nuisance parameter. We adopt a “fixed‐effects” approach that seeks to protect against any sequence of incidental parameters. We transform τ to (δ, ρ, ω), where δ is a J×K matrix of coefficients from the least‐squares projection of τ on a N×J matrix x of strictly exogenous variables, ρ is a K×K symmetric, positive semidefinite matrix obtained from the residual sums of squares and cross‐products in the projection of τ on x, and ω is a (N−J) ×K matrix whose columns are orthogonal and have unit length. The model is invariant under the actions of a group on the sample space and the parameter space, and we find a maximal invariant statistic. The distribution of the maximal invariant statistic does not depend upon ω. There is a unique invariant distribution for ω. We use this invariant distribution as a prior distribution to obtain an integrated likelihood function. It depends upon the observation only through the maximal invariant statistic. We use the maximal invariant statistic to construct a marginal likelihood function, so we can eliminate ω by integration with respect to the invariant prior distribution or by working with the marginal likelihood function. The two approaches coincide. Decision rules based on the invariant distribution for ω have a minimax property. Given a loss function that does not depend upon ω and given a prior distribution for (γ, δ, ρ), we show how to minimize the average—with respect to the prior distribution for (γ, δ, ρ)—of the maximum risk, where the maximum is with respect to ω. There is a family of prior distributions for (δ, ρ) that leads to a simple closed form for the integrated likelihood function. This integrated likelihood function coincides with the likelihood function for a normal, correlated random‐effects model. Under random sampling, the corresponding quasi maximum likelihood estimator is consistent for γ as N→∞, with a standard limiting distribution. The limit results do not require normality or homoskedasticity (conditional on x) assumptions.