https://rss.onlinelibrary.wiley.com/doi/pdf/10.2307/2344317

Asymptotically Efficient Rank Invariant Test Procedures

SUMMARY We wish to test a simple hypothesis against a family of alternatives indexed by a one-dimensional parameter, 0. We use a test derived from the corresponding family of test statistics appropriate for the case when 0 is given. Davies (1977) introduced this problem when these test statistics had normal distributions. The present paper considers the case when their distribution is chi-squared. The results are applied to the detection of a discrete frequency component of unknown frequency in a time series. In addition quick methods for finding approximate significance probabilities are given for both the normal and chi-squared cases and applied to the two-phase regression problem in the normal case.

Hypothesis testing when a nuisance parameter is present only under the alternative

An extension of the Wilcoxon rank-sum test is developed to handle the situation in which a variable is measured for individuals in three or more (ordered) groups and a non-parametric test for trend across these groups is desired. The uses of the test are illustrated by two examples from cancer research.

https://onlinelibrary.wiley.com/doi/pdf/10.1002/sim.4780140409

A wilcoxon-type test for trend

We introduce a goodness-of-fit process for quantile regression analogous to the conventional R2 statistic of least squares regression. Several related inference processes designed to test composite hypotheses about the combined effect of several covariates over an entire range of conditional quantile functions are also formulated. The asymptotic behavior of the inference processes is shown to be closely related to earlier p-sample goodness-of-fit theory involving Bessel processes. The approach is illustrated with some hypothetical examples, an application to recent empirical models of international economic growth, and some Monte Carlo evidence.

https://www.jstor.org/stable/pdfplus/2669943.pdf

Goodness of Fit and Related Inference Processes for Quantile Regression

The R package coin implements a unified approach to permutation tests providing a huge class of independence tests for nominal, ordered, numeric, and censored data as well as multivariate data at mixed scales. Based on a rich and flexible conceptual framework that embeds different permutation test procedures into a common theory, a computational framework is established in coin that likewise embeds the corresponding R functionality in a common S4 class structure with associated generic functions. As a consequence, the computational tools in coin inherit the flexibility of the underlying theory and conditional inference functions for important special cases can be set up easily. Conditional versions of classical tests---such as tests for location and scale problems in two or more samples, independence in two- or three-way contingency tables, or association problems for censored, ordered categorical or multivariate data---can easily be implemented as special cases using this computational toolbox by choosing appropriate transformations of the observations. The paper gives a detailed exposition of both the internal structure of the package and the provided user interfaces along with examples on how to extend the implemented functionality.

/pdf/implementing-a-class-of-permutation-pests-the-coin-package-5dlprxrxhq.pdf

J. Hajek

Papers

The Theory of Rank Tests.