An Empirical Study of Convergence Rates and Resampling-based Confidence Interval Methods For Step Threshold Linear Regression Models

Abstract

This thesis studies the convergence rates of maximum likelihood estimators and coverage probabilities of resampling-based confidence intervals of parameters in step threshold linear regression models through Monte Carlo experiments under five different data generating models. The results suggest that when the data is not generated from a step threshold model, the convergence rate of the threshold estimator is cubic root n at large sample sizes as theory indicates. In terms of coverage probabilities of the confidence intervals, the results show that the optimal block size for m-out-of-n bootstrap or subsampling depends on whether the model is correctly specified.