Numerical treatment of restricted gauss-markov model 1

The singular value decomposition (SVD) has been widely used in the ordinary linear model and other statistical problems. In this paper, we shall introduce the generalized singular value decomposition (GSVD) of any two matrices X and H having the same number of columns to moti-vate the numerical treatment of large scale restricted Gauss-Markov model (y,Xβ\Hβ = r,σ²1), a situation to reveal the relationship (or restriction) existing among the parameters of the model. Many approaches to restricted linear model are already available. Those approaches apply the generalized inverse of matrices and emphasize the the-oretical solution of the problem rather than the development of efficient and numerical stable algorithm for the computation of estimators. The possible merit of the method present here might lie in the facts that they directly lead to an efficient, numerically stable and easily programmed algorithm for     

Testing for a change lit the regression matrix of a multivariate linear model

A Bayesian test procedure Is developed to test; the null hypothesis of no change In the regression matrix of a multivariate lin¬ear model against the alternative hypothesis of exactly one change The resulting test is based on the marginal posterior distribution of the change point; To illustrate the test procedure a numerical example using a bivariate regression model is considered.     

How effective are the reset tests for omitted variables

In regression analysis, RESET has widely been regarded as an effective diagnostic test especially for omitted variables. This paper investigates the limitations of the existing RESET tests in detecting omitted variables. We analyze the sources from which RESET draws its power and point out the circumstances under which RESET will likely be ineffective. We offer some Monte Carlo evidence as well as an empirical application to illustrate the weaknesses of the RESET tests. A more robust RESET type test is proposed.     

A comparison of the mixture and classification approaches to cluster analysis

This paper examines the relative performance of two commonly used clustering methods based on maximum likelihood in the context of classifying a sample of observations of unknown origin arising from two normal populations with a common covariance matrix. the associated properties of the two methods are compared by conducting a series of simulation experiments under both mixture and separate sampling schemes.     

全站仪对边测量测站点位置的选择

根据全站仪对边测量原理，推导其精度公式，确定影响精度的主要因素，采用模拟数据分析对边测量精度状况以及与测站点位置的关系，指出有利的测站点位置，结论对现场测量工作有指导意义。     

求解铸件凝固问题的一种新方法

用线性摄动法给出了铸件在表面形状呈正弦变化的有限厚度铸型上凝固的三维热传导问题的数学模型，结合自变量变换法与有限差分法求解了热传导方程的数值解，给出了相变面随时间的变化过程和铸件的温度场分布情况．     

Confidence regions for parameters in linear models with additional information

Using given significant additional information it is possible to improve different confidence regions for the regression parameters in a linear model. Thereby, the given informations may concern the expectation and (or) the variance of the observations, and an improvement is possible in the sense of the decrease of the confidence regions' size. In particular it is possible to improve the so called confidence ellipsoids which are often used to estimate the considered parameters.     

The optimal Lp norm estimator in linear regression models

The least squares estimator is usually applied when estimating the parameters in linear regression models. As this estimator is sensitive to departures from normality in the residual distribution, several alternatives have been proposed. The L_p norm estimators is one class of such alternatives. It has been proposed that the kurtosis of the residual distribution be taken into account when a choice of estimator in the L_p norm class is made (i.e. the choice of p). In this paper, the asymtotic variance of the estimators is used as the criterion in the choice of p. It is shown that when this criterion is applied, other characteristics of the residual distribution than the kurtosis (namely moments of order p-2 and 2p-2) are important.     

Robust small area estimation

Small area estimation has received considerable attention in recent years because of growing demand for small area statistics. Basic area‐level and unit‐level models have been studied in the literature to obtain empirical best linear unbiased prediction (EBLUP) estimators of small area means. Although this classical method is useful for estimating the small area means efficiently under normality assumptions, it can be highly influenced by the presence of outliers in the data. In this article, the authors investigate the robustness properties of the classical estimators and propose a resistant method for small area estimation, which is useful for downweighting any influential observations in the data when estimating the model parameters. To estimate the mean squared errors of the robust estimators of small area means, a parametric bootstrap method is adopted here, which is applicable to models with block diagonal covariance structures. Simulations are carried out to study the behaviour of the proposed robust estimators in the presence of outliers, and these estimators are also compared to the EBLUP estimators. Performance of the bootstrap mean squared error estimator is also investigated in the simulation study. The proposed robust method is also applied to some real data to estimate crop areas for counties in Iowa, using farm‐interview data on crop areas and LANDSAT satellite data as auxiliary information. The Canadian Journal of Statistics 37: 381–399; 2009 © 2009 Statistical Society of Canada