Comparison study on some classical lack-of-fit tests in regression models

Abstract

The relationship between a random variable and a random vector is often investigated through the regression modeling. Because of its relative simplicity and ease of interpretation, a particular parametric form is often assumed for the regression function. If the pre-specified function form truly reflects the truth, then the resulting estimators and inference procedures would be reliable and efficient. But if the regression function does not represent the true relationship between the response and the predictors, then the inference results might be very misleading. Therefore, lack-of-fit test should be an indispensable part in regression modeling. This report compares the finite sample performance of several classical lack-of-fit tests in regression models via simulation studies. It has three chapters. The conception of the lack-of-fit test, together with its basic setup, is briefly introduced in Chapter 1; then several classical lack-of-fit test procedures are discussed in Chapter 2; finally, thorough simulation studies are conducted in Chapter 3 to assess the finite sample performance of each procedure introduced in Chapter 2. Some conclusions are also summarized in Chapter 3. A list of MATLAB codes that are used for the simulation studies is given in the appendix.