SOME REMARKS ON THE MEAN, MEDIAN, MODE AND SKEWNESS

Many sufficient conditions for inequalities about the mean, median, mode and skewness have been obtained. The paper presents a theorem that unifies already known results, gives some counter-examples, and considers the cases of Pearson distributions.     

A Berry–Esséen Bound for M-estimators

We prove a Berry–Esséen bound for general M-estimators under optimal regularity conditions on the score function and the underlying distribution. As an application we obtain Berry–Esséen bounds for the sample median, the L_p -median, p > 1 and Huber's estimator of location     

考虑管理弹性的项目成本估算方法

针对项目成本超支问题,考虑项目的实际运作,将管理弹性的价值添加到项目管理中,力求更好地估计项目成本,最终使项目成本得到控制。抓住成本控制中"人"的因素,在给定项目运作方式的基础上,采用反应控制机制,得到更好的项目成本估算,有效地解决项目成本失控问题。     

制造企业主营业务利润质量评价模型研究

制造企业主营业务利润质量是衡量企业整体盈利质量的重要内容,以国资委45家制造企业数据为例,用主成分多元统计分析方法建立制造企业主营业务利润质量评价模型,通过实证归纳得出影响制造企业利润质量最重要的因素是企业对成本的管理和控制能力的结论。     

Analysis of longitudinal multiple-source binary data using generalized estimating equations

Summary.  We present a multivariate logistic regression model for the joint analysis of longitudinal multiple-source binary data. Longitudinal multiple-source binary data arise when repeated binary measurements are obtained from two or more sources, with each source providing a measure of the same underlying variable. Since the number of responses on each subject is relatively large, the empirical variance estimator performs poorly and cannot be relied on in this setting. Two methods for obtaining a parsimonious within-subject association structure are considered. An additional complication arises with estimation, since maximum likelihood estimation may not be feasible without making unrealistically strong assumptions about third- and higher order moments. To circumvent this, we propose the use of a generalized estimating equations approach. Finally, we present an analysis of multiple-informant data obtained longitudinally from a psychiatric interventional trial that motivated the model developed in the paper.     

一类热传导方程的H1-Galerkin混合有限元分析

采用H1 Galerkin混合有限元方法对一类热传导方程的初边值问题,提出了半离散H1 Galerkin混合有限元格式,通过误差分析,得到H1 Galerkin混合有限元解与真解的L2模和H1模的最优阶误差估计.     

Quality Control Chart for the Mean using Double Ranked Set Sampling

In this paper, an attempt is made to develop Quality Control Charts for monitoring the process mean based on Double Ranked Set Sampling (DRSS) rather than the traditional Simple Random Sampling (SRS). Considering a normal population and several shift values, the performance of the Average Run Length (ARL) of these new charts was compared with the control charts based on Ranked Set Sampling (RSS) and SRS with the same number of observations. It is shown that the new charts do a better job of detecting changes in process mean compared with SRS and RSS.     

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.     

Multilevel models for longitudinal data

Summary.  Repeated measures and repeated events data have a hierarchical structure which can be analysed by using multilevel models. A growth curve model is an example of a multilevel random-coefficients model, whereas a discrete time event history model for recurrent events can be fitted as a multilevel logistic regression model. The paper describes extensions to the basic growth curve model to handle auto-correlated residuals, multiple-indicator latent variables and correlated growth processes, and event history models for correlated event processes. The multilevel approach to the analysis of repeated measures data is contrasted with structural equation modelling. The methods are illustrated in analyses of children's growth, changes in social and political attitudes, and the interrelationship between partnership transitions and childbearing.     

The strong uniform convergence of multivariate variable kernel estimates

We show that sup, completely as, where f is a uniformly continuous density on are independent random vectors with common density f, and f_n is the variable kernel estimate Here H_ni is the distance between X_i and its kth nearest neighbour, K is a given density satisfying some regularity conditions, and k is a sequence of integers with the property that log asn