Non-parametric tests that deal with two samples include scores tests (such as the Wilcoxon rank sum test, normal scores test, log istic scores test, Cauchy scores test, etc.) and Fisher’s randomization test. B ecause the non-parametric tests generally require a large amount of computational work, there are few studies on small-sample properties, although asymptotic properties with regard to var...

In order to check that a parametric model provides acceptable tail approximations, we present a test which compares the parametric estimate of an extreme upper quantile with its semiparametric estimate obtained by extreme value theory. To build this test, the sampling variations of these estimates are approximated through parametric bootstrap. Numerical Monte Carlo simulations explore the cover...

Test procedures are constructed for testing the goodness-of-fit in parametric regression models. The test statistic is in the form of an L2 distance between the empirical characteristic function of the residuals in a parametric regression fit and the corresponding empirical characteristic function of the residuals in a non-parametric regression fit. The asymptotic null distribution as well as t...

To test for equality of variances given two independent random samples from univariate normal populations, popular choices would be the two-sample F test and Levene’s test. The latter is a nonparametric test while the former is parametric: it is the likelihood ratio test, and also a Wald test. Another Wald test of interest is based on the difference in the sample variances. We give a nonparamet...

The Mann-Kendall test is a commonly-used nonparametric test for time trend. However, the standard P-values obtained from it are based on an assumption of independence between observations (since the theory is that of the Kendall correlation). However, observations in time series are often autocorrelated: knowing that one observation is larger than the mean may tell you that the next observation...

We propose a way of testing exogeneity of an explanatory variable without any parametric assumptions in the presence of a conditional "instrumental variable". A testable implication is derived that if an explanatory variable is exogenous, the conditional distribution of the outcome given explanatory variables is independent of the instrumental variable. We propose a consistent nonparametric boo...