关于齐次马氏信源二元函数的一类偏差定理

利用任意信源相对熵密度偏差的概念,使用分析的方法研究了齐次马氏信源的一类强偏差定理,得出了一个二元函数的一类强偏差定理和几个极限性质.     

可编程控制器在洁净空调自动控制系统中的应用

介绍了可编程控制器(PLC)在洁净空调控制系统中应用的实例，对应用中遇到的问题提出了解决方案，并对PLC在洁净空调系统中推广使用的前景进行了分析。     

De l'unicité des estimateurs robustes en régression lorsque le paramètre d'échelle et le paramètre de la régression sont estimés simultanément

Several methods have been suggested to calculate robust M- and G-M -estimators of the regression parameter β and of the error scale parameter σ in a linear model. This paper shows that, for some data sets well known in robust statistics, the nonlinear systems of equations for the simultaneous estimation of β, with an M-estimate with a redescending ψ-function, and σ, with the residual median absolute deviation (MAD), have many solutions. This multiplicity is not caused by the possible lack of uniqueness, for redescending ψ-functions, of the solutions of the system defining β with known σ; rather, the simultaneous estimation of β and σ together creates the problem. A way to avoid these multiple solutions is to proceed in two steps. First take σ as the median absolute deviation of the residuals for a uniquely defined robust M-estimate such as Huber's Proposal 2 or the L₁-estimate. Then solve the nonlinear system for the M-estimate with σ equal to the value obtained at the first step to get the estimate of β. Analytical conditions for the uniqueness of M and G-M-estimates are also given.     

DOMAIN ESTIMATION IN FINITE POPULATIONS1

This paper suggests unbiased estimators (UE's) for the size, mean and total of a domain, with specific features, in a given finite population on the basis of simple random sampling without replacement (SRSWOR) continued till a preassigned number of domain members is observed.     

Asymptotic posterior normality for multiparameter problems

For asymptotic posterior normality in the one-parameter cases, Weng [2003. On Stein's identity for posterior normality. Statist. Sinica 13, 495–506] proposed to use a version of Stein's Identity to write the posterior expectations for functions of a normalized quantity in a form that is more transparent and can be easily analyzed. In the present paper we extend this approach to the multi-parameter cases and compare our conditions with earlier work. Three examples are used to illustrate the application of this method.     

The failure of meta-analytic asymptotics for the seemingly efficient estimator of the common risk difference

We consider the case of a multicenter trial in which the center specific sample sizes are potentially small. Under homogeneity, the conventional procedure is to pool information using a weighted estimator where the weights used are inverse estimated center-specific variances. Whereas this procedure is efficient for conventional asymptotics (e. g. center-specific sample sizes become large, number of center fixed), it is commonly believed that the efficiency of this estimator holds true also for meta-analytic asymptotics (e.g. center-specific sample size bounded, potentially small, and number of centers large). In this contribution we demonstrate that this estimator fails to be efficient. In fact, it shows a persistent bias with increasing number of centers showing that it isnot meta-consistent. In addition, we show that the Cochran and Mantel-Haenszel weighted estimators are meta-consistent and, in more generality, provide conditions on the weights such that the associated weighted estimator is meta-consistent.     

Penalized contrast estimator for adaptive density deconvolution

The authors consider the problem of estimating the density g of independent and identically distributed variables X_I, from a sample Z₁,… Z_n such that Z_I = X_I + σ? for i = 1,…, n, and E is noise independent of X, with σ? having a known distribution. They present a model selection procedure allowing one to construct an adaptive estimator of g and to find nonasymptotic risk bounds. The estimator achieves the minimax rate of convergence, in most cases where lower bounds are available. A simulation study gives an illustration of the good practical performance of the method.     

Approximating bayesian inference by weighted likelihood

The author proposes to use weighted likelihood to approximate Bayesian inference when no external or prior information is available. He proposes a weighted likelihood estimator that minimizes the empirical Bayes risk under relative entropy loss. He discusses connections among the weighted likelihood, empirical Bayes and James‐Stein estimators. Both simulated and real data sets are used for illustration purposes.     

A robust prediction error criterion for pareto modelling of upper tails

Estimation of the Pareto tail index from extreme order statistics is an important problem in many settings. The upper tail of the distribution, where data are sparse, is typically fitted with a model, such as the Pareto model, from which quantities such as probabilities associated with extreme events are deduced. The success of this procedure relies heavily not only on the choice of the estimator for the Pareto tail index but also on the procedure used to determine the number k of extreme order statistics that are used for the estimation. The authors develop a robust prediction error criterion for choosing k and estimating the Pareto index. A Monte Carlo study shows the good performance of the new estimator and the analysis of real data sets illustrates that a robust procedure for selection, and not just for estimation, is needed.     

Corrected proof of the result of 'A prediction error property of the Lasso estimator and its generalization' by Huang (2003)

The Lasso achieves variance reduction and variable selection by solving an ?₁‐regularized least squares problem. Huang (2003) claims that ‘there always exists an interval of regularization parameter values such that the corresponding mean squared prediction error for the Lasso estimator is smaller than for the ordinary least square estimator’. This result is correct. However, its proof in Huang (2003) is not. This paper presents a corrected proof of the claim, which exposes and uses some interesting fundamental properties of the Lasso.