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     

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．     

A GENEALOGY OF CORRESPONDENCE ANALYSIS

Over the past half a century correspondence analysis has grown from a little known statistical technique designed to graphically depict the association structure of categorical variables that form a contingency table to a very popular tool used in a wide variety of disciplines. Despite this growth, correspondence analysis remains relatively unknown in some parts of the world, including the Australasian statistical community. This paper provides a non‐technical, bibliographic exploration of correspondence analysis. We take a step back to view the development of this statistical technique and provide a brief account of its genealogy with a selection of over 270 key publications that have contributed to its growth. We also look at its maturity over the decades.     

The Impact of Measurement Error on Principal Component Analysis

We investigate the effect of measurement error on principal component analysis in the high‐dimensional setting. The effects of random, additive errors are characterized by the expectation and variance of the changes in the eigenvalues and eigenvectors. The results show that the impact of uncorrelated measurement error on the principal component scores is mainly in terms of increased variability and not bias. In practice, the error‐induced increase in variability is small compared with the original variability for the components corresponding to the largest eigenvalues. This suggests that the impact will be negligible when these component scores are used in classification and regression or for visualizing data. However, the measurement error will contribute to a large variability in component loadings, relative to the loading values, such that interpretation based on the loadings can be difficult. The results are illustrated by simulating additive Gaussian measurement error in microarray expression data from cancer tumours and control tissues.     

Perturbation diagnostics of autocorrelation coefficients in non linear mixed-effects models with AR(1) errors based on M-estimation

In this work we propose and analyze non linear mixed-effects models for longitudinal data, which are widely used in the fields of economics, biopharmaceuticals, agriculture, and so on. A robust method to obtain maximum likelihood estimates for the parameters is presented, as well as perturbation diagnostics of autocorrelation coefficient in non linear models based on robust estimates and influence curvature. The obtained results are illustrated by plasma concentrations data presented in Davidian and Giltinan, which was analyzed under the non robust situation.     

A simulation study of deterministic ridge estimators

Some deterministic ridge rules are proposed and their finite sample properties are studied. Further, a simulation study is also conducted. Based on the simulation results, the proposed ridge estimators can improve the mean squared error over the least squares estimator, provided that the condition number of correlation matrices in the regression model is large, say at least 1,000.     

The homotopy perturbation method for the Black–Scholes equation

The homotopy perturbation method is designed to obtain a quick and accurate solution to the Black–Scholes equation and boundary conditions for a European option pricing problem. The problem of pricing a European option can be cast a partial differential equation. The analytical solution of the equation is calculated in the form of a convergent power series with easily computable components.     

Local influence in box-cox transformation for multivariate regression data

The Box-Cox power family of transformations for multivariate regression data is considered. The influence of cases on the maximum likelihood estimators of the transformation parameters is investigated using the local influence approach, An example is given to- illustrate the local influence method and to show the effectiveness of the method.     

Extremes of Determinants and Optimality of Canonical Variables

Extremes of quadratic forms have been presented by several authors (Okamoto, 1969; Rao, 1973; Seber, 1984). The obvious multivariate extension of the extreme of quadratic forms is the extreme of the determinants as well as the ratios of the determinants. In this paper we develop some supremums of the determinants and the ratios of the determinants. A new optimality and equations of canonical variables are obtained.     

Methods for diagnosing multiplicative-interaction models for two-way contingency tables

An expanded class of multiplicative-interaction (M-I) models is proposed for two-way contingency tables. These models a generalization of Goodman's association models, fill in the gap between the independence and the saturated models. Diagnostic rules based on a transformation of the data are proposed for the detection of such models. These rules, utilizing the singular value decomposition of the transformed data, are very easy to use. Maximum likelihood estimation is considered and the computational algorithms discussed. A data set from Goodman (1981) and another from Gabriel and Zamir (1979) are used to demostrate the diagnostic rules.