Statistical Inference On Normal Population When Mean Of Some Variables Varies With Group

Repeated measurements(RM) analysis refer to the pooling of observations on a cross-section of households,firms,etc over several time periods.They are widely used in many fields,for example,the social sciences,finance and so on. For RM data from normal distribution,the observations are often transformed by an orthogonal matrix. By observing the characteristic of transformed data,we put forward our question.Let p x 1 random vector series X₁,..., X_n which are distributed according to multivariate normal distribution with common and unknown covariance matrix E.Let X_i^' be partitioned as (X_ij¹' ,X_ij²' )' such that X_ij¹ is a m × 1 vector i = 1,...,n, j=1,..., q.Let X₁₁²,..., X_nq² be independent and identical distribution with unknown mean vector μ² and X_{n1+...+nj-1+1, j}¹,... ,X_n1+...+nj,j¹ be i.i.d with unknown mean vector μ_j¹, j= 1, ..., q.This thesis is devoted to studying how to estimate μ₁¹ ,... ,μ_q¹ and covariance matrix ∑ with μ_j¹ varying when covariance matrix S is general.Six aspects of work are considered.The first aspect gives the practical background of question.The second gives maximun likelihood estimation of parameters by conditional distribution and regression method.The third discusses some propositions of parameter estimation.The fourth gives likelihood ratio test statistic for testing μ₁¹= ...= μ_q¹ .The fifth considers covariance test which is put forward in chapter one.The finial a sample is given.