A Simple Method to Obtain all the Sample-Values and their Probabilities of the Wald-Wolfowitz Test Statistics in the Existence of Ties

In order to carry out non-conservative tests in the general two-sample problem with ties, we want to know all possible sample-values of the used test statistics and their occurrence probabilities as well. But this knowledge can be acquired only after very protracted attempts. In the present paper we depict a simple technique for obtaining that without any exertion in the case of the Wald-Wolfowitz test statistic. With that, we then are able to lead the Wald-Wolfowitz test easily and effortlessly in any manner conservative or non-conservative and in the existence of any number and any length of ties.     

Tests for Ordered Alternatives with Right Censored Data

A procedure is presented to test for ordered alternatives in the k-sample case when the observations are subject to right censorship. This procedure is an extension of the one proposed by Hettmansperger and Norton (1987). The nondecreasing and umbrella alternatives are of particular interest. A Monte Carlo simulation study is done comparing this procedure with two other existing ones in the nondecreasing case.     

On the use of comparison regions in visualizing stochastic uncertainty in some two-parameter estimation problems

When considering simultaneous inference for two parameters, it is very common to visualize stochastic uncertainty by plotting two-dimensional confidence regions. This allows us to test post hoc null hypotheses about a single point in a simple manner. However, in some applications the interest is not in rejecting hypotheses on single points, but in demonstrating evidence for the two parameters to be in a convex subset of the parameter space. The specific convex subset to be considered may vary from one post hoc analysis to another. Then it is of interest to have a visualization allowing to perform corresponding analyses. We suggest comparison regions as a simple tool for this task.     

Maximally Selected Rank Statistics for Dose‐Response Problems

We consider the bivariate situation of some quantitative, ordinal, binary or censored response variable and some quantitative or ordinal exposure variable (dose) with a hypothetical effect on the response. Data can either be the outcome of a planned dose‐response experiment with only few dose levels or of an observational study where, for example, both exposure and response variable are observed within each individual. We are interested in testing the null hypothesis of no effect of the dose variable vs. a dose‐response function depending on an unknown ‘threshold’ parameter. The variety of dose‐response functions considered ranges from no observed effect level (NOEL) models to umbrella alternatives. Here we discuss generalizations of the method of Lausen & Schumacher (Biometrics, 1992, 48, 73–85)which are based on combinations of two‐sample rank statistics and rank statistics for trend. Our approach may be seen as a generalization of a proposal for change‐point problems. Using the approach of Davies (Biometrika, 1987, 74, 33–43)we derive and approximate the asymptotic null distribution for a large number of thresholds considered. We use an improved Bonferroni inequality as approximation for a small number of thresholds considered. Moreover, we analyse the small sample behaviour by means of a Monte‐Carlo study. Our paper is illustrated by examples from clinical research and epidemiology.     

Robust Umbrella Tests for a Generalized Behrens-Fisher Problem

This paper is concerned with testing for umbrella alternatives in a k-sample location problem when the underlying populations have possibly different shapes. Following CHEN and WOLFE (1990b), rank-based modifications of the HETTMANSPERGER-NORTON (1987) tests are considered for both the settings where the peak of the umbrella is known and where it is unknown. The proposed procedures are exactly distribution-free when the continuous populations are identical with any shape. Moreover, the modified test for peak-known umbrella alternatives remains asymptotically distribution-free when the continuous populations are assumed to be symmetric, even if they differ in shapes. Comparative results of a Monte Carlo study are presented.     

Valid historical data for probabilistic risk analysis in natural disasters

With the changes in the nature and the society, risks will inevitably change. It implies that, with the passage of time, some historical data would be invalid for probabilistic risk analysis. In this paper, a model to acquire the valid data is suggested, which is based on the Mann- Kendall test to detect abrupt change-point on time series data. What's more, the typhoon risk analysis in Guangdong Province, China is used as a case study to show how to apply the model. The valid data of the intensities of typhoons and the related losses in the province for the probabilistic risk analysis is obtained from the data during the time from 1984 to 2012. Comparing with the results based on the set of invalid data and the set of all collected data, the assessed risk based on the valid data is more reliable, which could reflect the dynamics of the typhoon risk.     

Robustness of Statistical Tests in the Two-Sample Location Problem

A simulation study was performed to compare three statistical tests with respect to their performances in the two-sample location problem for contaminated normal distributions. The three tests were: the t-test, the rank-transformed t-test, and the Wilcoxon rank-sum test. The results showed the t-test to be inferior to the other two tests.     

An Approximate Solution to the Behrens-Fisher Problem

An approximate and practical solution is proposed for the Behrens-Fisher problem. This solution is compared to the solutions considered by Mehta and Srinivasan (1970) and Welch's (1937) approximate t-test in terms of the stability of the size and magnitude of the power. It is shown that the stability of the size of the new test is better than that of Welch's t when at least one of the sample sizes is small. When the sample sizes are moderately large or large the sizes and powers of all the recommended tests are almost the same.