Statistical Inference On Contrasts In Means Of Two-Component Linear Mixed Models

The two-component linear mixed model is a special form of linear mixed model. And it is often used in the statistical analysis of repeated measurement data such as longitudinal data,panel data, and genetic data. In recent years, some studies found that a lot of data are not normal,and the observations are sometimes missing at random for various reasons. This dissertation is combined with skew-normal distribution and missing data to study the statistical inference under two-component linear mixed model, focusing on the contrasts in means.Firstly, we consider the statistical inference on contrasts in means of two-component linear mixed model with missing data in Chapter 3. The condition that random effects are normal is relaxed. Through a proper transformation can obtain the reduced model. Thus statistical inference on all contrasts in means can be reduced to corresponding inference on the new parameters. The estimator of parameters and exact test statistic were proposed. Some numerical simulations are given to illustrate the superiority and robustness of exact test statistic.Secondly, we considers the statistical inference on contrasts in means of two-component linear mixed models with skew-normal random errors in Chapter 4. It is proved that the estimator of the variance parameters is still unbiased under skew-normal error. And the exact test statistic follow F distribution when the corresponding null hypothesis is true. Furthermore, the power and size of F-test are compared with normal error and skew-normal error. Some numerical simulations are given to illustrate our results that the statistic also have excellent properties under skew-normal error.Finally, the robustness of F-test were further explored from the numerical simulation.