| This dissertation considers higher-order performance of bootstrap methods for standard tests. The first article investigates the nonparametric block bootstrap for Lagrange Multiplier (LM) tests and Likelihood Ratio (LR)-type tests of nonlinear restrictions. The second article considers the restricted parametric bootstrap for percentile t tests, Wald tests, LM tests, and LR-type tests. The main objective throughout this dissertation is to look into effectiveness of bootstrap methods in improving finite sample performance of standard tests based on asymptotic critical values, and to analytically verify the exact magnitudes of bootstrap improvements depending on various testing schemes.; Chapter 2 establishes higher-order improvements of the nonparametric block bootstrap for LM tests and LR-type tests of nonlinear restrictions. The improvements take the form of reduced errors in test rejection probabilities. The chapter extends results of Andrews (1999) to provide new results for LM and LR-type tests based on extremum estimators, such as generalized method of moments (GMM) estimators and maximum likelihood (ML) estimators. The results cover the nonparametric iid bootstrap and non-overlapping and overlapping block bootstraps. The magnitude of the higher-order improvements for both tests are shown to be the same as those for Wald tests. Simulation evidence based on a simple linear regression model supports the theoretical findings.; Chapter 3 establishes higher-order improvements of the restricted parametric bootstrap tests for Markov-type strong mixing observations. Bounds on the errors in rejection probabilities are obtained for percentile t, Wald, LM, and LR-type tests, based on ML estimators. For symmetric percentile t, Wald, LM, and LR-type tests, the bounds show that the restricted parametric bootstrap performs as well as the (unrestricted) parametric and nonparametric bootstraps for iid observations. For one-sided and equal-tailed percentile t tests, the restricted parametric bootstrap outperforms the unrestricted parametric bootstrap. The bounds obtained are sharper than those established in Andrews (2002b). With the restricted parametric bootstrap, the errors in rejection probability are shown to be O(N−3/2) for the one-sided or equal-tailed percentile t tests and O( N−2) for the symmetric t, Wald, and LM tests, where N is the sample size. The bootstrap improvements are confirmed by small simulation experiments using a binary logit model. |
