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Statistic Analysis of Finite Mixture Models

Author: QianHui
Tutor: ZongXuPing
School: Yangzhou University
Course: Applied Mathematics
Keywords: Hybrid model of exponential family EM algorithm Linear model Likelihood Ratio Test Asymptotic distribution
CLC: O212
Type: Master's thesis
Year: 2007
Downloads: 131
Quote: 3
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Abstract


Hybrid model can be complex and changeable effective model of random phenomena , in recent years , increasing attention has been paid . Many people this had a strong interest in the natural sciences , medicine, engineering , making the hybrid model even in the anthropology field has a very wide range of applications . mixed model does not satisfy the usual regularity conditions , however , the likelihood good than the test the asymptotic nature as well as the distribution of the test statistic nature are difficult to estimate , the application of numerical methods mixed is still a huge challenge in the statistical model , we encountered a lot of difficulties in the study of the model test of homogeneity on the issue . finite mixture distribution density function of this article , we discuss a mixed model of exponential family EM algorithm, the likelihood ratio test potential function analog , the asymptotic distribution of the test statistic and linear regression with a mixture of exponential family distribution given in Chapter II of the abstract form of the EM algorithm , EM algorithm is a hybrid model greatly likelihood estimates of standard tools , this paper systematically introduces how to use the EM algorithm for solving the problem of maximum likelihood estimation , introduced a mixed model of exponential family EM algorithm iteration formula Chapter four hybrid model calculation of the likelihood ratio test quantiles of the statistic , and the inspection of the simulation of the potential function . , we can see that globally maximizing the likelihood function method is not necessarily good potential , under the null hypothesis by a simple EM algorithm the starting law often can not find the global maximum, but can be a very good trend . fourth chapter we consider a class of hybrid model for g ( x ) = ( 1 - ξ) f ( the x θ 1 < / sub>) ξf (x, θ 2), 0 ≤ ξ ≤ 1, where f is a given probability density function , obtained the model likelihood ratio asymptotic distribution of the statistic Chapter exponential family mixed combined distribution and linear model , we focus on the residual analysis and impact analysis of the model , the exponential family mixture distribution to get a better application in the linear model problem .

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CLC: > Mathematical sciences and chemical > Mathematics > Probability Theory and Mathematical Statistics > Mathematical Statistics
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