The Statistical Inference Of The Parameters When The Corelation Structure Is Given

In this thesis,we mainly interested in the statistics inference on parameters when the correlation structure is given as:(1)The correlation matrix is a linear combination of some known matrices;(2)The inverse of the correlation matrix is a linear combination of some known matrices;(3)The correlation matrix is a block diagonal matrix,and the sub-matrices on the diagonal can be linearly expressed by some known matrices;(4)The correlation matrix is a block diagonal matrix,and the inverse of the sub-matrices on the diagonal can be linearly expressed by some known matrices.Many scientific studies often collect data resulting from experiments in which responses have been recorded repeatedly over time and examine how the response depends on subject-specific characteristics.The resulting data are referred to as longitudinal data.The main features of longitudinal data is that observations from different subjects are independent,those from the same subject at different time points are dependent.The estimators under working correlation structure misspecification,can severely affect the corresponding efficiency.Therefore,the most important task for longitudinal data analysis is how to identify the correlation among subjects correctly.In recent years,longitudinal data analysis has been one of the hot issues in statistical research.It is of great significance to study the statistical inference on parameters when the correlation structure is given.The generalized estimating equation(GEE)approach proposed by Liang and Zeger is perhaps one of the most widely used methods for longitudinal data analysis.While the GEE method guarantees the consistency of its estimators under working correlation structure misspecification,the corresponding efficiency can be severely affected.In this paper,we propose a two-step estimation method in which the structure of the correlation matrix is assumed to be given.Briefly,the first step is to obtain the parameter estimates by solving the quasi-likelihood equations with the correlation matrix being summed to be known,and the second step is to find the estimate of the correlation structure by minimizing the difference between the empirical estimate and the correlation structure model given the parameter estimates from step 1.Steps 1 and 2are run iteratively until convergence.Asymptotic properties of the two-step estimators are developed.We illustrate the methodology with data analysis and simulation studies.And then,we discussed the implementation of the proposed method for unbalanced data.Finally,we provides a concluding discussion.