Combination of distribution-free tests for the general two-sample problem with application to the social sciences

ABSTRACT

The problem of detecting any differences between the distributions of two populations is addressed within the non parametric permutation framework of combined tests. Combined testing has been very useful to address the location, the scale, and the location/scale problems. The aim of the paper is to see whether combined testing is useful also for the general two-sample problem. The framework of combined testing for the general two-sample problem is presented and some tests are proposed. These tests are valid even when a non random sample of units is randomized into two groups. Type 1 error rate and power characteristics of the new tests are investigated and compared to former tests. It is shown that the new tests compare favorably with the former ones. An application to a very important socioeconomic problem is discussed.     

The optimal group size using inverse binomial group testing considering misclassification

ABSTRACT

Inverse binomial sampling is preferred for quick report. It is also recommended when the population proportion is really small to ensure a positive sample is contained. Group testing has been discussed extensively under binomial model, but not so much under negative binomial model. In this study, we investigate the problem of how to determine the group size using inverse binomial group testing. We propose to choose the optimal group size by minimizing asymptotic variance of the estimator or the cost relative to Fisher information. We show the good performance of our estimator by applying to the data of Chlamydia.     

Johansen cointegration rank tests under local alternative hypotheses when related drift or linear trend is not dependent upon sample size in VARs

Abstract

This paper discusses Johansen’s likelihood ratio tests to determine the cointegration rank under local alternative hypotheses in the vector autoregressive models (VARs) in which drift or linear trend related to the hypotheses is not dependent upon the sample size, and evaluates related asymptotic properties. We show that the test statistics diverge at the rate of the sample size even under one of local alternative hypotheses, owing to the existence of such a deterministic term. This implies that under our situations, the tests are far more powerful than those under the conventional local alternative hypotheses.     

An Asymptotic Characterization of Finite Degree U-statistics With Sample Size-Dependent Kernels: Applications to Nonparametric Estimators and Test Statistics

We provide a simple result on the H-decomposition of a U-statistics that allows for easy determination of its magnitude when the statistic’s kernel depends on the sample size n. The result provides a direct and convenient method to characterize the asymptotic magnitude of semiparametric and nonparametric estimators or test statistics involving high dimensional sums. We illustrate the use of our result in previously studied estimators/test statistics and in a novel nonparametric R² test for overall significance of a nonparametric regression model.     

A generalized p-value approach to inference on the performance measures of an M/Ek/1 queueing system

Abstract

The hypothesis tests of performance measures for an M/E_k/1 queueing system are considered. With pivotal models deduced from sufficient statistics for the unknown parameters, a generalized p-value approach to derive tests about parametric functions are proposed. The focus is on derivation of the p-values of hypothesis testing for five popular performance measures of the system in the steady state. Given a sample T, let p(T) be the p values we developed. We derive a closed form expression to show that, for small samples, the probability P(p(T) ? γ) is approximately equal to γ, for 0 ? γ ? 1.     

Group testing with test error as a function of concentration

A common assumption in group testing applications is that there is no test error, i.e., misclassification of a single item or a group of items cannot occur. Graff and Roeloffs ( 1972 ) have proposed a procedure applicable when there is a known probability of misclassification. We generalize their results to the situation where the probability of misclassification depends on the proportion of defective items in the group.     

Balancing type I and type II error probabilities: further comments on proof of safety vs proof of hazard

This paper elaborates on earlier contributions of Bross (1985) and Millard (1987) who point out that when conducting conventional hypothesis tests in order to “prove” environmental hazard or environmental safety, unrealistically large sample sizes are required to achieve acceptable power with customarily-used values of Type I error probability. These authors also note that “proof of safety” typically requires much larger sample sizes than “proof of hazard”. When the sample has yet to be selected and it is feared that the sample size will be insufficient to conduct a reasonable.     

Testing equality of location parameters of two exponential distributions from censored samples

A modification to Tiku's (1981) test, which may be seriously biased, is proposed. The modified test is only marginally biased if at all and is substantially more powerful. A ratio test based on Tiku’s (1967) modified likelihood function is also proposed, and shown to have power comparable to the power of the ratio test based on the likelihood function. The proposed ratio test is, however, much easier from a computational viewpoint.