ABSTRACT
This chapter reviews standard Gaussian-theory inference on one sample location models. It presents motivation for why a distribution-free approach to location testing is necessary, and presents nonparametric techniques for inference on quantiles. The chapter discusses the techniques for estimating a single cumulative distribution function. Observations from the Laplace distribution give a level close to the targeted level. Observations from the Cauchy distribution give a level much smaller than the targeted level, which is paradoxical, because one might expect heavy tails to make it anti-conservative. The resulting density is bimodal, with tails lighter than one would otherwise expect. Values of the statistic for which the null hypothesis is not rejected are between the horizontal lines; log medians in the confidence intervals are values of the test statistic within this region.
