Likelihood Methods and Nonparametric Tests

Standard techniques of nonparametric statistics are related to likelihood procedures. In particular, rank tests and permutation tests in the regression problem are shown to be directly related to score function tests based on marginal and conditional likelihoods, respectively. The problem of estimating a population percentile is also examined from the viewpoint of marginal likelihood. These calculations tend to bring nonparametric procedures more closely in line with procedures adopted in parametric inference.