Assessing a hypothesis test for the difference between two quantiles from independent populations

An empirical distribution function estimator for the difference of order statistics from two independent populations can be used for inference between quantiles from these populations. The inferential properties of the approach are evaluated in a simulation study where different sample sizes, theoretical distributions, and quantiles are studied. Small to moderate sample sizes, tail quantiles, and quantiles which do not coincide with the expectation of an order statistic are identified as problematic for appropriate Type I error control.     

Bounds for expectations of concomitants

We present sharp bounds on expected values of concomitants based on a sample of identically distributed random pairs. The dependence between pair components is described by regression functions or modelled by copulas, or generated by sampling without replacement from finite populations.     

On Terrel's characterization of uniform distribution

Terrel (1983) (The Annals of Probability, Vol. 11, No. 3, 823–826) showed that the coefficient of correlation between the smaller and larger of a sample of size two is at most one-half, and this upper bound is attained only for continuous uniform distributions. His proof is of computational nature and is based on the properties of Legendre polynomials. We give an easier proof of Terrel's characterization and we show how our method can be used for obtaining sharper bounds within the class of discrete distributions onN points and also a characterization of the equidistant uniform distribution.     

Discrete distributions with maximum expected value of the maximum

We give an upper bound for the expected value of the largest order statistic of a simple random sample of size n from a discrete distribution on N points. We also characterize the distributions that attain such bound. In the particular case n=2, we obtain a characterization of the discrete uniform distribution. © 1998 Elsevier Science B.V. All rights reserved.     

Generalized order statistics from two parameter uniform distribution

In this paper some distributional properties of the generalized order statistics from uniform distribution are given. The minimum variance linear unbiased as well best ( in the sense of minimum mean squared error) invariant estimators of the parameters of the two parameter uniform distribution based on the first m generalized order statistics are presented.     

Exact conditional inference for two uniform populations

We discuss the nature of ancillary information in the context of the continuous uniform distribution. In the one-sample problem, the existence of sufficient statistics mitigates conditioning on the ancillary configuration. In the two-sample problem, additional ancillary information becomes available when the ratio of scale parameters is known. We give exact results for conditional inferences about the common scale parameter and for the difference in location parameters of two uniform distributions. The ancillary information affects the precision of the latter through a comparison of the sample value of the ratio of scale parameters with the known population value. A limited conditional simulation compares the Type I errors and power of these exact results with approximate results using the robust pooled t-statistic.     

Structure-preserving mappings of uniform order statistics

There are several well-known mappings which transform the first r common order statistics in a sample of size n from a standard uniform distribution to a full vector of dimension r of order statistics in a sample of size r from a uniform distribution. Continuing the results reported in a previous paper by the authors, it is shown that transformations of these types do not lead to order statistics from an i.i.d. sample of random variables, in general, when being applied to order statistics from non-uniform distributions. By accepting the loss of one dimension, a structure-preserving transformation exists for power function distributions.     

Isotonic inference for populations related to the uniform distribution

Consider the class of densities defined by Hogg and Craig (1956) and related to the uniform distribution, depending on an unknown parameter. Let there be k > 2 given populations yielding samples of unequal sizes from such densities. Now let a partial order on the set of the value defining the populations be given. we treat isotonic estimation, testing for order restrictins, and testing for homogeneity against order restrictions. The exact distrubutions of these tests turn out to be similar in structure to those for the normal distrubution case as iven in Barlow, Bartholomew, Bremner and Brunk (1972) and in Robertson and wegman (1978), in that they can be expressed as weighted chi square distributions. applications to selection and ranking methodlogy are pointed out.     

Non parametric hypothesis tests for comparing reliability functions

In reliability and related disciplines, comparing reliability functions of two (or more) aging processes is a crucial step in the process of determining reliability and understanding an aging process. The aim of this paper is to propose a non parametric statistical methodology to compare two populations based on their mean residual life function and expected inactivity time function. We introduce some novel hypothesis testing procedures that involve both Cramér–von Mises- and Kolmogorov–Smirnov-type test statistics and their decision rules are constructed based on the asymptotic distributions of these test statistics and bootstrapping method. We study the practical behavior of the proposed testing procedures extensively through simulations. The results reveal that the proposed hypothesis testing procedures perform efficiently in identifying small and large differences. Two real-life examples are discussed to demonstrate the practical utility of the tests.     

Ranked set sample sign test for quantiles

A ranked set sample version of the sign test is proposed for testing hypotheses concerning the quantiles of a population characteristic. Both equal and unequal allocations are considered and the relative performance of different allocations is assessed in terms of Pitman's asymptotic relative efficiency. In particular, for each quantile, the allocation that maximizes the efficacy is identified and shown to not depend on the population distribution.     

Sign test for ranked-set sampling

The exact null distribution of the ranked-set sample (RSS) sign test statistic is computed. The power of this test is compared with the simple random sample (SRS) sign test for some continuous symmetric distributions. The problem of imperfect judgement is discussed. The superiority of RSS over SRS is demonstrated.     

Multiple hypothesis test for parameter constancy based on recursive residuals

This article presents a multiple hypothesis test procedure that combines two well known tests for structural change in the linear regression model, the CUSUM test and the recursive t test. The CUSUM test is run through the sequence of recursive residuals as usual; if the CUSUM plot does not violate the critical lines, one more step is taken to perform the t test for hypothesis of zero mean based on all recursive residuals. The asymptotic size of this multiple hypothesis test is derived; power simulation results suggest that it outperforms the traditional CUSUM test and complements other tests that are currently stressed in econometrics.     

A statistical test for the hypothesis of Gaussian random function

A Gaussian random function is a functional version of the normal distribution. This paper proposes a statistical hypothesis test to test whether or not a random function is a Gaussian random function. A parameter that is equal to 0 under Gaussian random function is considered, and its unbiased estimator is given. The asymptotic distribution of the estimator is studied, which is used for constructing a test statistic and discussing its asymptotic power. The performance of the proposed test is investigated through several numerical simulations. An illustrative example is also presented.     

Two new estimators for the proportion of true null hypotheses in multiple test

In multiple hypothesis test, an important problem is estimating the proportion of true null hypotheses. Existing methods are mainly based on the p-values of the single tests. In this paper, we propose two new estimations for this proportion. One is a natural extension of the commonly used methods based on p-values and the other is based on a mixed distribution. Simulations show that the first method is comparable with existing methods and performs better under some cases. And the method based on a mixed distribution can get accurate estimators even if the variance of data is large or the difference between the null hypothesis and alternative hypothesis is very small.     

Multiple hypothesis test for parameter constancy based on recursive residuals

This article presents a multiple hypothesis test procedure that combines two well known tests for structural change in the linear regression model, the CUSUM test and the recursive t test. The CUSUM test is run through the sequence of recursive residuals as usual; if the CUSUM plot does not violate the critical lines, one more step is taken to perform the t test for hypothesis of zero mean based on all recursive residuals. The asymptotic size of this multiple hypothesis test is derived; power simulation results suggest that it outperforms the traditional CUSUM test and complements other tests that are currently stressed in econometrics.     

Fractiles of an extended multiple outlier test

The widely-used Tietjen—Moore multiple outlier statistic has a defect as originally proposed in that it may test the wrong observations as outliers. The defect is corrected by redefinition and the statistic extended to make use of possible additional information on underlying variance. Results of simulation of the revised statistic are presented.     

Optimal bounds on l-statistics based on samples drawn with replacement from finite populations

We describe a method of establishing optimal bounds on the expectations of arbitrary linear combinations of order statistics based on iid samples drawn with replacement from finite populations of a fixed size. The bounds are expressed in terms of the population size, mean, central absolute moments, and coefficients of the combination. The bounds are precisely determined for the trimmed means and their differences, and single order statistics and their differences in particular. We also show that with increase in population size, our bounds approach the respective universal ones for arbitrary iid samples.     

Asymptotic non-null distribution of a test of equality of exponential populations

In this paper further asymptotic expansions of the non-null distribution of the likelihood ratio criterion for testing the equality of several one parameter exponential distributions are obtained when the alternatives are close to the hypothesis. These expansions are obtained for the first time in terms of beta distributions.