Inferences about the Population Mean: Empirical Likelihood versus Bootstrap-t

Abstract

The problem of making inferences about the population mean, μ, is considered. Known theoretical results suggest that a Bartlett corrected empirical likelihood method is preferable to two basic bootstrap techniques: a symmetric two-sided bootstrap-t and an equal-tailed bootstrap-t. However, simulations in this study indicate that, when the sample size is small, these two bootstrap methods are generally better in terms of Type I errors and probability coverage. As the sample size increases, situations are found where the Bartlett corrected empirical likelihood method performs better than the equal-tailed bootstrap-t, but the symmetric bootstrap-t gives the best results. None of the four methods considered are always satisfactory in terms of probability coverage or Type I errors, particularly when dealing with skewed distributions where the expected proportion of points flagged as outliers is somewhat high. If this proportion is 0.14, for example, all four methods can be unsatisfactory even with n=300, but if sampling from a symmetric distribution or a skewed distribution with relatively light tails the results suggest using a symmetric two-sided bootstrap-t method.