VARIANCE ESTIMATION IN NONPARAMETRIC MULTIPLE REGRESSION

ABSTRACT

We consider the variance estimation in a general nonparametric regression model with multiple covariates. We extend difference methods to the multivariate setting by introducing an algorithm that orders the design points in higher dimensions. We also consider an adaptive difference estimator which requires much less strict assumptions on the covariate design and can significantly reduce mean squared error for small sample sizes.     

Random coefficients regression models. a review 1

A review is given of random regression coefficients models. The emphasis is put on the problem of estimating the mean regression coefficients and the covariance matrix of the coefficients. Prediction of the individual random coefficients is not discussed. The main purpose of the review is to point to the practical aspects of the models and the problem of statistical inference in finite samples. Some problems for future research are indicated.     

浅谈社会发展的双重结构模式

探索适合于研究发展中国家的社会结构模式 ,从而突破单一结构模式的现代化理论的局限性是本文的主旨。运用分析和比较的方法 ,指出社会结构具有多重性、多层次性 ,发展中国家的社会结构具有独特性。发展中国家只有形成社会表层结构与社会深层结构良性互动的模式 ,才能保持结构张力 ,焕发社会活力 ,促进社会发展。     

激光散斑相位差的条件统计分布与表面粗糙度的关系

在粗糙表面高度起伏服从高斯统计和表面服从圆型相关的情况下，分析了由弱散射体产生的远场高斯激光散斑相位差的条件统计分布与表面粗糙度的关系．     

中国红十字会救护总队部的"林可胜时期"(下)

救护总队部的“林可胜时期”(1938～1942年),是中国红十字会抗战救护最辉煌的时期。文章依据档案、当时的报刊、文献、口述历史资料及该会内部资料,考察了中国红十字会救护总队部的组建、空间及内部组织结构变迁、与卫训总所的关系以及“内部风潮”的潜滋暗长对抗战救护事业的多元效应,弥补了相关研究的不足。     

Data depth and correlation

Summary: We describe depth–based graphical displays that show the interdependence of multivariate distributions. The plots involve one–dimensional curves or bivariate scatterplots, so they are easier to interpret than correlation matrices. The correlation curve, modelled on the scale curve of Liu et al. (1999), compares the volume of the observed central regions with the volume under independence. The correlation DD–plot is the scatterplot of depth values under a reference distribution against depth values under independence. The area of the plot gives a measure of distance from independence. Correlation curve and DD-plot require an independence model as a baseline: Besides classical parametric specifications, a nonparametric estimator, derived from the randomization principle, is used. Combining data depth and the notion of quadrant dependence, quadrant correlation trajectories are obtained which allow simultaneous representation of subsets of variables. The properties of the plots for the multivariate normal distribution are investigated. Some real data examples are illustrated. *This work was completed with the support of Ca Foscari University.     

Convexity-based clustering criteria: theory,algorithms, and applications in statistics

This paper deals with the construction of optimum partitions of for a clustering criterion which is based on a convex function of the class centroids as a generalization of the classical SSQ clustering criterion for n data points. We formulate a dual optimality problem involving two sets of variables and derive a maximum-support-plane (MSP) algorithm for constructing a (sub-)optimum partition as a generalized k-means algorithm. We present various modifications of the basic criterion and describe the corresponding MSP algorithm. It is shown that the method can also be used for solving optimality problems in classical statistics (maximizing Csiszárs -divergence) and for simultaneous classification of the rows and columns of a contingency table.     

Admissible minimum bias estimation of response surfaces

The minimum bias estimator was introduced as an alternative to the least squares estimator for approximating response functions by low-order polynomials. Here we show how to obtain an admissible estimator with smaller squared bias.     

Second-Order Response Surface Model with Neighbor Effects

This article considers the second-order response surface model in which the experimental units, i.e., plots experience the neighbor effects from immediate left and right neighboring plots assuming the plots to be placed adjacent linearly with no gaps. Conditions have been derived for the estimation of coefficients of second-order response surface model. A method of constructing designs for fitting second-order response surface in the presence of neighbor effects has been developed. The designs so obtained are found to be rotatable.     

弯曲液面的临界光反射现象

实验中发现了弯曲液面的临界光反射现象,并采集到清晰的、对比度高的弯曲液面临界反射图样。在激光束斜入射的情况下,弯曲液面临界反射的图样中,有一椭圆状暗场,暗场附近区域有明亮清晰的条纹。根据几何光学的分析,解释了这一临界光反射现象。