Bootstrap Statistical Inference: Examples and Evaluations for Political Science

Abstract

Theory: Bootstrapping is a nonparametric approach to statistical inference that relies on large amounts of computation rather than mathematical analysis and distributional assumptions of traditional parametric inference. It has been shown to provide asymptotically accurate inferences for a wide variety of statistics. Hypothesis: Bootstrapping may make more accurate inferences than the parametric approach under two general circumstances: 1) when the assumptions of parametric inference are not tenable, and 2) when no parametric alternative exists for a problem. Methods: Monte Carlo simulation is used to test the performance of bootstrap and parametric confidence intervals for both types of situations in which bootstrapping is hypothesized to be superior to parametric inference. A single data example is used to illustrate the use of the bootstrap: a seats/votes model of U.S. House elections from 1932 to 1988. Results: My central conclusions are that in the cases examined: 1) bootstrap confidence intervals are at least as good as the parametric confidence interval and sometimes better, 2) OLS parametric confidence intervals do not perform too badly when the model error is non-normal, especially as sample size increases, and 3) when no parametric alternative exists, the bootstrap provides a reasonable method of making statistical inferences.