Optimal model averaging estimation for correlation structure in generalized estimating equations

Longitudinal data analysis requires a proper estimation of the within-cluster correlation structure in order to achieve efficient estimates of the regression parameters. When applying likelihood-based methods one may select an optimal correlation structure by the AIC or BIC. However, such information criteria are not applicable for estimating equation based approaches. In this paper we develop a model averaging approach to estimate the correlation matrix by a weighted sum of a group of patterned correlation matrices under the GEE framework. The optimal weight is determined by minimizing the difference between the weighted sum and a consistent yet inefficient estimator of the correlation structure. The computation of our proposed approach only involves a standard quadratic programming on top of the standard GEE procedure and can be easily implemented in practice. We provide theoretical justifications and extensive numerical simulations to support the application of the proposed estimator. A couple of well-known longitudinal data sets are revisited where we implement and illustrate our methodology.     

Exactly optimal sampling designs for processes with a product covariance structure

The author considers the problem of finding exactly optimal sampling designs for estimating a second‐order, centered random process on the basis of finitely many observations. The value of the process at an unsampled point is estimated by the best linear unbiased estimator. A weighted integrated mean squared error or the maximum mean squared error is used to measure the performance of the estimator. The author presents a set of necessary and sufficient conditions for a design to be exactly optimal for processes with a product covariance structure. Expansions of these conditions lead to conditions for asymptotic optimality.     

Optimal Circular Block Designs for Neighbouring Competition Effects

Competition or interference occurs when the responses to treatments in experimental units are affected by the treatments in neighbouring units. This may contribute to variability in experimental results and lead to substantial losses in efficiency. The study of a competing situation needs designs in which the competing units appear in a predetermined pattern. This paper deals with optimality aspects of circular block designs for studying the competition among treatments applied to neighbouring experimental units. The model considered is a four-way classified model consisting of direct effect of the treatment applied to a particular plot, the effect of those treatments applied to the immediate left and right neighbouring units and the block effect. Conditions have been obtained for the block design to be universally optimal for estimating direct and neighbour effects. Some classes of balanced and strongly balanced complete block designs have been identified to be universally optimal for the estimation of direct, left and right neighbour effects and a list of universally optimal designs for v<20 and r<100 has been prepared.     

优选论制约条件体系的全应效用和局部效用——从天津话的连读变调看OT语法的预测力

作为对生成语法的发展,优选论延续了对形式的描写及对普遍规则的探究,同时也摆脱了生成语法无法摆脱的局限性.指出:这种实证上的差异完全可以通过优选论制约条件的分合来加以解释和说明.从这一点上看,优选论既可以界定语言的总体类别,也可以说明语言内的变异情况,因而具有诸多以往音系学理论无法比拟的优势.     

On empirical bayes sequential estimation

We study the empirical Bayes approach to the sequential estimation problem. An empirical Bayes sequential decision procedure, which consists of a stopping rule and a terminal decision rule, is constructed for use in the component. Asymptotic behaviors of the empirical Bayes risk and the empirical Bayes stopping times are investigated as the number of components increase.     

On robust empirical bayes analysis of means and variances from stratified samples

Ghosh and Lahiri (1987a,b) considered simultaneous estimation of several strata means and variances where each stratum contains a finite number of elements, under the assumption that the posterior expectation of any stratum mean is a linear function of the sample observations - the so called“posterior linearity” property. In this paper we extend their result by retaining the “posterior linearity“ property of each stratum mean but allowing the superpopulation model whose mean as well as the variance-covariance structure changes from stratum to stratum. The performance of the proposed empirical Bayes estimators are found to be satisfactory both in terms of “asymptotic optimality” (Robbins (1955)) and “relative savings loss” (Efron and Morris (1973)).     

缺失数据下指数族分布参数的经验Bayes检验

文章在加权线性损失下讨论了带有非随机缺失数据连续型单参数指数族分布参数的经验Bayes检验问题.利用非参数插补的方法,重新构造了参数的经验Bayes检验函数,在适当的条件下证明了所提出的经验Bayes检验函数的渐近最优性,并获得了它的收敛速度.     

On Uniformly Optimal Networks: A Reversal of Fortune?

In this article, the general problem of comparing the performance of two communication networks is examined. The standard approach, using stochastic ordering as a metric, is reviewed, as are the mixed results on the existence of uniformly optimal networks (UONs) which have emerged from this approach. While UONs have been shown to exist for certain classes of networks, it has also been shown that no UON network exists for other classes. Results to date beg the question: Is the problem of identifying a Uniformly Optimal Network (UON) of a given size dead or alive? We reframe the investigation into UONs in terms of network signatures and the alternative metric of stochastic precedence. While the endeavor has been dead, or at least dormant, for some 20 years, the findings in the present article suggest that the question above is by no means settled. Specifically, we examine a class of networks of a particular size for which it was shown that no individual network was uniformly optimal relative to the standard metric (the uniform ordering of reliability polynomials), and we show, using the aforementioned alternative metric, that this class is totally ordered and that a uniformly optimal network exists after all. Optimality with respect to “performance per unit cost” type metrics is also discussed.     

An Optimal Retrospective Change Point Detection Policy

Abstract.  Since the middle of the twentieth century, the problem of making inferences about the point in a surveyed series of observations at which the underlying distribution changes has been extensively addressed in the economics, biostatistics and statistics literature. Cumulative sum-type statistics have commonly been thought to play a central role in non-sequential change point detections. Alternatively, we present and examine an approach based on the Shiryayev–Roberts scheme. We show that retrospective change point detection policies based on Shiryayev–Roberts statistics are non-asymptotically optimal in the context of most powerful testing.     

On the optimalizes of the mbgdd's under mixed effects model

In the present paper, under the assumption of a mixed effects model with random block effects, the type 1 optimality of the most balanced group divisible designs of type 1 has been established within the general class of all proper and connected block designs with k<v.