Asymptotic expansions for test statistics and tests for normality based on robust regression

This dissertation focuses on two different topics in econometrics. The first one is presented in Chapter 2 and is related to higher order asymptotic theory. The power of the Lagrange multiplier, Wald and likelihood ratio tests for the first order autoregressive model is compared through the approximations to the distributions of these three tests. The adequacy of the approximation is examined. The Wald and likelihood ratio tests are found to have superior performance than the Lagrange multiplier test. The comparisons are done according to stringency of the test statistics. As a second topic in Chapter 3, the dissertation examines the use of residuals from robust regression instead of OLS residuals in test statistics for the normality of the errors. According to simulation results their improvement over standard normality tests is found only in specialized circumstances. The applications on real data set show these conditions occur often enough in practice.