Inference on some linear mixed-effect models and testing lack-of-fit for experiments without replication

This dissertation contains two independent parts: (I) statistical inference on some linear mixed-effect models, and (II) testing lack-of-fit of linear regression models for experiments without replication.;Exact as well as approximate tests were proposed for analyzing data from unbalanced split-plot experiments. These tests utilize a matrix transformation which separates the mixed model into two independent models, each associated with a diagonal covariance matrix. The test statistics for testing various hypotheses are constructed based on these two transformed models. The proposed tests are simple in computation and have better or equal performance as that of SAS Mixed procedure under situations considered.;A group of three tests, namely the overall lack-of-fit, between-cluster lack-of-fit, and within-cluster lack-of-fit tests were proposed for testing the lack-of-fit of a linear regression model applied to experiments without replicates. The proposed tests are robust and adaptive to different ways of forming the clusters. The power of the proposed tests is significantly higher than those from the known tests under situations considered in this dissertation. Very importantly, currently only the proposed tests are capable of detecting which type of lack-of-fit is dominant when both between-cluster and within-cluster lack-of-fit are present.