Discussions On Contaminated Linear Models

Linear model is one of the most important branches, which develops earlier and concludes more theories in mathematical statistics. During the past several hundred years, linear model is not only active in theory research which develops deeply; but also applies widely in some fields such as industry and agriculture, meteorology and geology, economical management, medical affairs, educational psychology gradually. As a most popular part in the scientific research in the linear model, contaminated linear model attracts more eyes because of the widespread exist in actual life and has the very high value in the application.The contaminated data which like Censored data except for the different background and expressive form are also a kind of incomplete data. Statistical analysis on contaminated data has attracted statistician's attention long ago. As early as in the 1960's, Huber had studied the maximum likelihood estimation of contaminated data Gauss distribution under the least favorable case, and suggested the well-known Huber's distribution as a solution. The so-called Contaminated model is such one in which the distribution of population is unknown or at least partly unknown, and owing to the disturbance coming from another contaminated source we can only observe the contaminated data where the distributions of contaminated variables (or contaminated source) are usually assumed to be known. The aim of statistical analysis is mainly to estimate the contaminated ratio (or contaminated coefficient) and other parameters in model. In recent years, there have been great progress in the field.This paper firstly considered a group of contaminated normal distribution which is assumed by Huber in 1964:F_N,ε={f:F=(1-ε)N(0,1)+εg,g(?)F_s}Where s is an unknown contaminated coefficient and F₅ is a group ofone-dimensional probability density functions which are symmetrical about the zero point. On the basis of this model, we give a conclusion on the problems which have relations with contaminated model. Then we discuss the applications on the...