On the relation between Hodges-Lehmann efficiency and Pitman efficiency

The relation between Hodges–Lehmann efficiency and Pitman efficiency is studied in the context of testing one-sided hypotheses about a real-valued parameter. It is first shown that for tests based on sums of independently and identically distributed observations local Hodges-Lehmann efficiency is equivalent to Pitman efficiency. Then, it is proved that this equivalence also carries over to tests based on two broad classes of M -estimators for the location problem. In all cases considered explicit formulas of the Hodges-Lehmann efficacies are obtained.     

地质宏观判断方法在三峡船闸高边坡稳定分析中的应用

应用宏观地质分析方法，分析了影响船闸高边坡岩体稳定的内、外在因素，并对其稳定性进行了评价，提出了工程施工和工程处理应注意的主要问题。     

A Nonrandomized,Nonconservative Version of the Fisher Exact Test

The Fisher exact test has been unjustly dismissed by some as ‘only conditional,’ whereas it is unconditionally the uniform most powerful test among all unbiased tests, tests of size α and with power greater than its nominal level of significance α. The problem with this truly optimal test is that it requires randomization at the critical value(s) to be of size α. Obviously, in practice, one does not want to conclude that ‘with probability x the we have a statistical significant result.’ Usually, the hypothesis is rejected only if the test statistic's outcome is more extreme than the critical value, reducing the actual size considerably.

The randomized unconditional Fisher exact is constructed (using Neyman–structure arguments) by deriving a conditional randomized test randomizing at critical values c(t) by probabilities γ(t), that both depend on the total number of successes T (the complete-sufficient statistic for the nuisance parameter—the common success probability) conditioned upon.

In this paper, the Fisher exact is approximated by deriving nonrandomized conditional tests with critical region including the critical value only if γ (t) > γ₀, for a fixed threshold value γ₀, such that the size of the unconditional modified test is for all value of the nuisance parameter—the common success probability—smaller, but as close as possible to α. It will be seen that this greatly improves the size of the test as compared with the conservative nonrandomized Fisher exact test.

Size, power, and p value comparison with the (virtual) randomized Fisher exact test, and the conservative nonrandomized Fisher exact, Pearson's chi-square test, with the more competitive mid-p value, the McDonald's modification, and Boschloo's modifications are performed under the assumption of two binomial samples.     

Approximations of the critical region of the fbietkan statistic

The Friedman (1937) test for the randomized complete block design is used to test the hypothesis of no treatment effect among k treatments with b blocks. Difficulty in determination of the size of the critical region for this hypothesis is com¬pounded by the facts that (1) the most recent extension of exact tables for the distribution of the test statistic by Odeh (1977) go up only to the case with k6 and b6, and (2) the usual chi-square approximation is grossly inaccurate for most commonly used combinations of (k,b). The purpose of this paper 2 is to compare two new approximations with the usual x² and F large sample approximations. This work represents an extension to the two-way layout of work done earlier by the authors for the one-way Kruskal-Wallis test statistic.     

Weighted combinations of rank tests for location-scale alternatives

All existing location-scale rank tests use equal weights for the components. We advocate the use of weighted combinations of statistics. This approach can partly be substantiated by the theory of locally most powerful tests. We specifically investi= gate a Wilcoxon-Mood combination. We give exact critical values for a range of weights. The asymptotic normality of the test statistic is proved under a general hypothesis and Chernoff-Savage conditions. The asymptotic relative efficiency of this test with respect to unweighted combinations shows that a careful choice of weights results in a gain in efficiency.     

Two-Sample Tests Based on the Integrated Empirical Process

Abstract

Let X ₁, …, X _m and Y ₁, …, Y _n be independent random variables, where X ₁, …, X _m are i.i.d. with continuous distribution function (df) F, and Y ₁, …, Y _n are i.i.d. with continuous df G. For testing the hypothesis H ₀: F = G, we introduce and study analogues of the celebrated Kolmogorov–Smirnov and one- and two-sided Cramér-von Mises statistics that are functionals of a suitably integrated two-sample empirical process. Furthermore, we characterize those distributions for which the new tests are locally Bahadur optimal within the setting of shift alternatives.     

A network algorithm for the exact treatment of the 2×k contingency table

A common statistical problem encountered in biomedical research is to test the hypothesis that the parameters of k binomial populations are all equal. An exact test of significance of this hypothesis is possible in principle, the appropriate null distribution being a normalized product of k binomial coefficients. However, the problem of computing the tail area of this distribution can be formidable since it requires the enumeration of all sets of k binomial coefficients whose product is less than a given constant. Existing algorithms, all of which rely on explicit enumeration to generate feasible binomial coefficients     

Testing hypotheses about the common mean of two normal populations

Two simple tests which allow for unequal sample sizes are considered for testing hypothesis for the common mean of two normal populations. The first test is an exact test of size a based on two available t-statistics based on single samples made exact through random allocation of α among the two available t-tests. The test statistic of the second test is a weighted average of two available t-statistics with random weights. It is shown that the first test is more efficient than the available two t-tests with respect to Bahadur asymptotic relative efficiency. It is also shown that the null distribution of the test statistic in the second test, which is similar to the one based on the normalized Graybill-Deal test statistic, converges to a standard normal distribution. Finally, we compare the small sample properties of these tests, those given in Zhou and Mat hew (1993), and some tests given in Cohen and Sackrowitz (1984) in a simulation study. In this study, we find that the second test performs better than the tests given in Zhou and Mathew (1993) and is comparable to the ones given in Cohen and Sackrowitz (1984) with respect to power..