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Publication bias undermines the results of meta‐analyses and other systematic reviews. Applying a formal test for publication bias is therefore a part of many protocols for conducting a meta‐analysis. To be effective in this role, the tests must have good power to detect the presence of publication bias. We derive the local limiting power functions and study the Pitman relative efficiency for two popular tests, Begg's and Egger's tests. The analysis suggests that the differences between the two arise out of built‐in robustness properties of Begg's test. These work to its detriment in the commonly used Gaussian model, but leave it with better efficiency when study effects are heavy‐tailed or skew. [ABSTRACT FROM AUTHOR]

We develop analogs of a class of weighted empirical minimum distance estimators of the underlying parameters in errors-in-variables linear regression models, when the regression error distribution and the conditional distribution of conditionally centered measurement error, given the surrogate, are symmetric around the origin. This class of estimators is defined as the minimizers of integrals of the square of a certain symmetrized weighted empirical process of the residuals. It includes the least absolute deviation (LAD) and an analog of the Hodges–Lehmann (H–L) estimators. In this paper we first develop this class of estimators when the distributions of the true covariates and measurement errors are known, and then extend them to the case when these distributions are unknown but validation data is available. In the case of Gaussian errors and covariates, the Pitman's asymptotic relative efficiency of the LAD and analog of the H–L estimators, relative to the bias corrected least square estimator, tends to infinity as the variances of the components of the measurement error vector tend to infinity. The findings of a simulation study that is included also show significant superiority of these two estimators over the bias corrected least squares estimator. • A class of minimum distance parameter estimators is developed in linear EIVs models. • The class includes the absolute deviation and an analog of the Hodges–Lehmann estimators. • The proposed estimators are more efficient than the bias corrected least square estimator. [ABSTRACT FROM AUTHOR]

In this paper, a general class of non-parametric tests for testing homogeneity of location parameter against umbrella alternatives is proposed. Testing for umbrella alternatives has many applications in the field of biology, medicine, botany, dose level testing, engineering, economics, psychology, zoology. As an example, the effectiveness of a drug is likely to increase with increase of dose up to a certain level and then its effect begins to decrease. The proposed test is based on linear combination of two-sample U-statistics. The null distribution of the test statistics is developed. We compare the test with some other competing tests in terms of Pitman asymptotic relative efficiency. To see execution of the test, a numerical example is provided. Simulation study is carried out to assess the power of proposed class of tests.

Many sampling methods allow the study of species richness and diversity in biological communities, but it is not known whether a single method can determine both the number and diversity of species in an unbiased and efficient way. Here we assess whether the least biased and most efficient method to determine reptile species richness in a Mexican dry scrubland is also the best method to estimate species diversity. The local assemblage was composed of 10 species, with the Mexican mud turtle (Kinosterton integrum) and the Jalapa spiny lizard (Sceloropus jalapae) being the dominant ones. Microhabitat surveys (MHS) were the most accurate and the most efficient method to estimate species richness, but they over–estimated species diversity (+67.1 %) as much as the other sampling methods, i.e., transect surveys and pitfall–trap stations, under–estimated it (–59 %). Our study shows that the best sampling method to determine the number of species in local assemblages may not be the best method to study species diversity. Although combining different sampling methods can increase the project costs in terms of time, effort and money, the use of structured inventories is recommended for the analysis of species diversity.

We initiate the study of goodness-of-fit testing for data consisting of positive definite matrices. Motivated by the appearance of positive definite matrices in numerous applications, including factor analysis, diffusion tensor imaging, volatility models for financial time series, wireless communication systems, and polarimetric radar imaging, we apply the method of Hankel transforms of matrix argument to develop goodness-of-fit tests for Wishart distributions with given shape parameter and unknown scale matrix. We obtain the limiting null distribution of the test statistic and a corresponding covariance operator, show that the eigenvalues of the operator satisfy an interlacing property, and apply our test to some financial data. We establish the consistency of the test against a large class of alternative distributions and derive the asymptotic distribution of the test statistic under a sequence of contiguous alternatives. We obtain the Bahadur and Pitman efficiency properties of the test statistic and establish a modified version of Wieand's condition. [ABSTRACT FROM AUTHOR]

We apply the method of Hankel transforms to develop goodness-of-fit tests for gamma distributions with given shape parameters and unknown rate parameters. We derive the limiting null distribution of the test statistic as an integrated squared Gaussian process, obtain the corresponding covariance operator and oscillation properties of its eigenfunctions, show that the eigenvalues of the operator satisfy an interlacing property, and make applications to two data sets. We prove consistency of the test, provide numerical power comparisons with alternative tests, study the test statistic under several contiguous alternatives, and obtain the asymptotic distribution of the test statistic for gamma alternatives with varying rate or shape parameters and for certain contaminated gamma models. We investigate the approximate Bahadur slope of the test statistic under local alternatives, and we establish the validity of the Wieand condition under which approaches through the approximate Bahadur and the Pitman efficiencies are in accord. [ABSTRACT FROM AUTHOR]

Pitman efficiency is the oldest known efficiency. Most of the known results for computing the Pitman efficiency take the form of bounds. Based on some recent developments due to the authors and some calculus of variations, we develop tools for computing the Pitman efficiency exactly. Their use is illustrated numerically.

Let X1,..., Xn be a sequence of independent and identically distributed random variables with an unknown underlying continuous cumulative distribution function F. Relative to this unknown distribution function suppose one would like to test a null hypothesis concerning the goodness of fit of F to some distribution function using symmetric functions of sample spacings. In some applications the null hypothesis is simple while in others it may be composite. In this article we present the large sample theory of tests based on symmetric functions of sample spacings under composite null hypotheses and contiguous alternatives. It is shown that these test statistics have the same asymptotic distribution in the case when parameters must be estimated from the sample as in the case when parameters are specified. Optimal goodness of fit tests are also constructed for these hypotheses. © 1992.

The efficiency concepts of Bahadur and Pitman are used to compare the Wilcoxon tests in paired and independent survey samples. A comparison through the length of corresponding confidence intervals is also done. Simple conditions characterizing the dominance of a procedure are derived. Statistical tests for checking these conditions are suggested and discussed. [ABSTRACT FROM AUTHOR]

We consider a recurrent event wherein the inter-event times are independent and identically distributed with a common absolutely continuous distribution function F. In this article, interest is in the problem of testing the null hypothesis that F belongs to some parametric family where the q-dimensional parameter is unknown. We propose a general Chi-squared test in which cell boundaries are data dependent. An estimator of the parameter obtained by minimizing a quadratic form resulting from a properly scaled vector of differences between Observed and Expected frequencies is used to construct the test. This estimator is known as the minimum chi-square estimator. Large sample properties of the proposed test statistic are established using empirical processes tools. A simulation study is conducted to assess the performance of the test under parameter misspecification, and our procedures are applied to a fleet of Boeing 720 jet planes' air conditioning system failures. [ABSTRACT FROM AUTHOR]

The Gini methodology in statistical inference and related area has got much attention in recent years. In this paper, using a characterisation based on the Gini index we develop a nonparametric test for testing exponentiality against new better than used in expectation class. We derive the exact null distribution of the proposed test statistic and then calculate the critical values for different sample sizes. Asymptotic properties of the test statistic are discussed. The test is compared with some other test by evaluating Pitman's asymptotic efficacy. We also discuss how to incorporate right-censored observations in our study. A simulation study is presented to demonstrate the performance of the testing method. Finally, we illustrated our test procedure using two real data sets. [ABSTRACT FROM AUTHOR]

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This article introduces the exchangeable Kendall's tau as a nonparametric intraclass association measure in a clustered data frame and studies the sampling properties of an estimator of this quantity. Its asymptotic distribution is derived under a multivariate exchangeable model. Two applications of the proposed statistic are considered. The first is an estimator of the intraclass correlation coefficient for data drawn from an elliptical distribution. The asymptotic properties of this estimator are investigated under an extended random effects ANOVA model. The second is a semiparametric intraclass independence test based on the exchangeable Kendall's tau whose performance is assessed using Pitman efficiencies and a Monte Carlo study. The Canadian Journal of Statistics 42: 384-403; 2014 © 2014 Statistical Society of Canada [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with hierarchical data having three levels. The level 1 units are nested in the level 2 units or subclusters which are themselves nested in the level 3 clusters. The model for this data is assumed to fulfill some symmetry assumptions. The level 1 units within each subcluster are exchangeable and a permutation of the subclusters belonging to the same cluster leaves the model unchanged. We are interested in measuring the dependence associated to clusters and subclusters respectively. Two exchangeable Kendall’s tau are proposed as non parametric measures of these two associations and estimators for these measures are proposed. Their asymptotic properties are then investigated under the proposed hierarchical model for the data. These statistics are then used to estimate the intra-class correlation coefficients for data drawn from elliptical hierarchical distributions. Hypothesis tests for the cluster and subcluster effects based on the proposed estimators are developed and their performances are assessed using Pitman efficiencies and a Monte Carlo study. [Copyright &y& Elsevier]

Statistics based on spacings, or the gaps between points, have been widely used in many contexts, primarily in testing goodness of fit. This paper derives Edgeworth-type asymptotic expansions for the sum of functions ofs-step spacings wheres, the order of spacings, may increase together with the sample sizen. Whensis fixed, it is known that only the Greenwood test, based on the sum of squares of these spacings, is first-order asymptotically efficient. In contrast, it is shown here that ifsgoes to infinity, there exist many other tests which are first-order efficient. We introduce and study the second-order efficiency of such tests and show that ifsis sufficiently large relative ton, the Greenwood test is no longer second-order efficient. Interestingly, we see that the common phenomenon of first-order efficiency implying second-order efficiency does not hold true in this situation. [ABSTRACT FROM AUTHOR]

We study allocations that maximize the power of tests of equality of two treatments having binary outcomes. When a normal approximation applies, the asymptotic power is maximized by minimizing the variance, leading to a Neyman allocation that assigns observations in proportion to the standard deviations. This allocation, which in general requires knowledge of the parameters of the problem, is recommended in a large body of literature. Under contiguous alternatives the normal approximation indeed applies, and in this case the Neyman allocation reduces to a balanced design. However, when studying the power under a noncontiguous alternative, a large deviations approximation is needed, and the Neyman allocation is no longer asymptotically optimal. In the latter case, the optimal allocation depends on the parameters, but is rather close to a balanced design. Thus, a balanced design is a viable option for both contiguous and noncontiguous alternatives. Finite sample studies show that a balanced design is indeed generally quite close to being optimal for power maximization. This is good news as implementation of a balanced design does not require knowledge of the parameters. [ABSTRACT FROM PUBLISHER]

Abstract: This paper considers the one-sample sign test for population quantiles in general ranked set sampling, and proposes a weighted sign test because observations with different ranks are not identically distributed. It is shown analytically that optimal weight always improves the Pitman efficiency for all distributions. For each quantile, the sampling allocation that maximizes the sign test efficacy is identified and shown to not depend on the population distribution. Moreover, distribution-free confidence intervals for quantiles based on ordered values of optimal ranked set samples are discussed. [Copyright &y& Elsevier]

Abstract: We show that under different moment bounds on the underlying variables, bootstrap approximation to the large deviation probabilities of standardized sample sum, based on independent random variables, is valid for a wider zone of , the sample size, compared to the classical normal tail probability approximation. As an application, different notions of efficiency for statistical tests are considered from Bayesian point of view. In particular, efficiency due to Pitman (1938) , Chernoff (1952) , and Bayes risk efficiency due to Rubin and Sethuraman (1965) turn out to be special cases with the choice of the weight function; i.e., prior density times loss. [Copyright &y& Elsevier]

In missing data problems, it is often the case that there is a natural test statistic for testing a statistical hypothesis had all the data been observed. A fuzzy p-value approach to hypothesis testing has recently been proposed which is implemented by imputing the missing values in the “complete data” test statistic by values simulated from the conditional null distribution given the observed data. We argue that imputing data in this way will inevitably lead to loss in power. For the case of scalar parameter, we show that the asymptotic efficiency of the score test based on the imputed “complete data” relative to the score test based on the observed data is given by the ratio of the observed data information to the complete data information. Three examples involving probit regression, normal random effects model, and unidentified paired data are used for illustration. For testing linkage disequilibrium based on pooled genotype data, simulation results show that the imputed Neyman Pearson and Fisher exact tests are less powerful than a Wald-type test based on the observed data maximum likelihood estimator. In conclusion, we caution against the routine use of the fuzzy p-value approach in latent variable or missing data problems and suggest some viable alternatives. [ABSTRACT FROM AUTHOR]

Consider testing whether F = F0 for a continuous cdf on R = (-∞,∞) and for a random sample X1,… , Xn from F. We derive expansions of the associated asymptotic power based on the Cramer-von Mises, Kolmogorov-Smirnov and Kuiper statistics. We provide numerical illustrations using a double-exponential example with a shifted alternative. [ABSTRACT FROM AUTHOR]

Nonparametric procedures for testing and estimation of the shape matrix in the case of multivariate elliptic distribution are considered. Testing for sphericity is an important special case. The tests and estimates are based on the spatial sign and rank covariance matrices. The estimates based on the spatial sign covariance matrix and symmetrized spatial sign covariance matrix are Tyler's [A distribution-free M-estimator of multivariate scatter, Ann. Statist. 15 (1987), pp. 234-251] shape matrix and and Dumbgen's [On Tyler's M-functional of scatter in high dimension, Ann. Inst. Statist. Math. 50 (1998), pp. 471-491] shape matrix, respectively. The test based on the spatial sign covariance matrix is the sign test statistic in the class of nonparametric tests proposed by Hallin and Paindaveine [Semiparametrically efficient rank-based inference for shape. I. Optimal rank-based tests for sphericity, Ann. Statist. 34 (2006), pp. 2707-2756]. New tests and estimates based on the spatial rank covariance matrix are proposed. The shape estimates introduced in the paper play an important role in the inner standardisation of the spatial sign and rank tests for multivariate location. Limiting distributions of the tests and estimates are reviewed and derived, and asymptotic efficiencies as well as finite-sample efficiencies of the proposed tests are compared with those of the classical modified John's [Some optimal multivariate tests, Biometrika 58 (1971), pp. 123-127; The distribution of a statistic used for testing sphericity of normal distributions, Biometrika 59 (1972), pp. 169-173] test and the van der Waerden test (Hallin and Paindaveine, [Semiparametrically efficient rank-based inference for shape. I. Optimal rank-based tests for sphericity, Ann. Statist. 34 (2006), pp. 2707-2756]). The symmetrised spatial sign- and rank-based estimates and tests seem to have a very high efficiency in the multivariate normal case, and they are much better than the classical estimate (shape matrix based on the regular covariance matrix) and test (John's test) for distributions with heavy tails. [ABSTRACT FROM AUTHOR]

Blest (2000, Aust. N. Z. J. Stat. 42, 101–111) proposed a new measure of rank correlation that is sensitive to discrepancies in the small ranks. This paper investigates the efficiency properties of non-parametric tests for independence based on Blest's correlation coefficient and its modifications. Pitman efficiency comparisons are made with analogous tests existing in the literature. Conditions for Pitman optimality of the Blest-type tests are established. [ABSTRACT FROM AUTHOR]

Classical univariate measures of asymmetry such as Pearson’s (mean-median)/σ or (mean-mode)/σ often measure the standardized distance between two separate location parameters and have been widely used in assessing univariate normality. Similarly, measures of univariate kurtosis are often just ratios of two scale measures. The classical standardized fourth moment and the ratio of the mean deviation to the standard deviation serve as examples. In this paper we consider tests of multinormality which are based on the Mahalanobis distance between two multivariate location vector estimates or on the (matrix) distance between two scatter matrix estimates, respectively. Asymptotic theory is developed to provide approximate null distributions as well as to consider asymptotic efficiencies. Limiting Pitman efficiencies for contiguous sequences of contaminated normal distributions are calculated and the efficiencies are compared to those of the classical tests by Mardia. Simulations are used to compare finite sample efficiencies. The theory is also illustrated by an example. [ABSTRACT FROM AUTHOR]

For general linear models with normally distributed random errors, the probability of a Type II error decreases exponentially as a function of sample size. This potentially rapid decline reemphasizes the importance of performing power calculations. [ABSTRACT FROM AUTHOR]

New test statistics are proposed for testing whether two random vectors are independent. Gieser and Randles, as well as Taskinen, Kankainen, and Oja have introduced and discussed multivariate extensions of the quadrant test of Blomqvist. This article serves as a sequel to this work and presents new multivariate extensions of Kendall's tau and Spearman's rho statistics. Two different approaches are discussed. First, interdirection proportions are used to estimate the cosines of angles between centered observation vectors and between differences of observation vectors. Second, covariances between affine-equivariant multivariate signs and ranks are used. The test statistics arising from these two approaches appear to be asymptotically equivalent if each vector is elliptically symmetric. The spatial sign versions are easy to compute for data in common dimensions, and they provide practical, robust alternatives to normal-theory methods. Asymptotic theory is developed to approximate the finite-sample null distributions as welt, as to calculate limiting Pitman efficiencies. Small-sample null permutation distributions are also described. A simple simulation study is used to compare the proposed tests with the classical Wilks test. Finally, the theory is illustrated by an example. [ABSTRACT FROM AUTHOR]

Kendall's τ for univariate samples is extended to the multivariate case using unit direction vectors in place of signs. Depending on whether the design matrix is fixed, this statistic yields a test for the multivariate analysis of variance or multivariate regression. Test of independence based on this statistic are easy, efficient, and robust. Its asymptotic properties and its Pitman efficiency are studied. In addition, some useful algebra in multiple dimensions is presented. [ABSTRACT FROM AUTHOR]

A robust estimator is developed for the location and scale parameters of a location-scale family. The estimator is defined as the minimizer of a minimum distance function that measures the distance between the ranked set sample empirical cumulative distribution function and a possibly misspecified target model. We show that the estimator is asymptotically normal, robust, and has high efficiency with respect to its competitors in literature. It is also shown that the location estimator is consistent within the class of all symmetric distributions whereas the scale estimator is Fisher consistent at the true target model. The paper also considers an optimal allocation procedure that does not introduce any bias due to judgment error classification. It is shown that this allocation procedure is equivalent to Neyman allocation. A numerical efficiency comparison is provided. [Copyright &y& Elsevier]

This paper develops a non-parametric multi-sample inference for simple-tree alternatives for ranked-set samples. The multi-sample inference provides simultaneous one-sample sign confidence intervals for the population medians. The decision rule compares these intervals to achieve the desired type I error. For the specified upper bounds on the experiment-wise error rates, corresponding individual confidence coefficients are presented. It is shown that the testing procedure is distribution-free.To achieve the desired confidence coefficients for multi-sample inference, a nonparametric confidence interval is constructed by interpolating the adjacent order statistics. Interpolation coefficients and coverage probabilities are provided, along with the nominal levels. [ABSTRACT FROM AUTHOR]

In a number of special cases, it has been shown that categorization of a continuous explanatory variable for use in a regression model can lead to efficiency losses. Nevertheless, categorization remains a popular remains of dealing with continuous variables, particularly in medical statistics. Two topics of current interest in medical statistics are subgroup effects in clinical trials and gene-environment interactions in genetic studies. In a regression model setting, these topics involve the examination of interaction effects, often between a binary explanatory variable and a continuous explanatory variable. In this article the efficiency losses associated with dichotomization of a continuous explanatory variable for the testing of such interaction effects are calculated and compared with those associated with the testing of main effects. It is shown that considerable additional efficiency loss can arise because of dichotomization in both a main effect and an interaction. The theoretical development is done in the context of exponential family models, thus also generalizing earlier results on efficiency loss for main effects. Some indication is also given of the losses in efficiency associated with more detailed categorization. The further impact of censoring in time-to-event models is investigated and shown to not alter the qualitative conclusions. The practical importance of the findings is illustrated through the analysis of data from a clinical trial in patients with prostate cancer. [ABSTRACT FROM AUTHOR]

In this paper multivariate extensions of the Friedman and Page tests for the comparison of several treatments are introduced. Related unadjusted and adjusted treatment effect estimates for the multivariate response variable are also found and their properties discussed. The test statistics and estimates are analogous to the traditional univariate methods. In test constructions, the univariate ranks are replaced by multivariate spatial ranks (J. Nonparam. Statist. 5 (1995) 201). Asymptotic theory is developed to provide approximations for the limiting distributions of the test statistics and estimates. Limiting efficiencies of the tests and treatment effect estimates are found in the multivariate normal and t distribution cases. The tests are rotation invariant only, but affine invariant versions can be easily constructed. The theory is illustrated by an example. [Copyright &y& Elsevier]

The use of statistical methods based on ranked-set sampling can lead to a substantial improvement over analog methods associated with simple random sampling schemes. This article develops a rank-based estimator and testing procedures for linear models for ranked-set samples. The estimator is defined as the minimizer of the rank dispersion function with Wilcoxon scores. It is shown that the estimator of the regression parameter is asymptotically normal and has higher Pitman asymptotic efficiency than a simple random-sample rank regression estimator. Three testing procedures are developed to test a general linear hypothesis: dispersion, Wald, and aligned rank tests. It is shown that all of these test statistics converge to a chi-squared distribution and the aligned rank test reduces to a simple random-sample analog of Kruskal-Wallis test for one-way analysis of variance. Under the assumption of perfect judgment ranking, optimal allocation of order statistics are constructed for set sizes smaller than 7. The optimal allocation procedures quantify middle observation(s) for symmetric unimodal distributions and smallest (largest) observation for right- (left-) skewed distributions. [ABSTRACT FROM AUTHOR]

This paper presents a class of sub-sample rank-sum statistics to test the stochastic ordering between two distributions. The proposed class includes as special case the min–max test of Öztürk. It is shown that the asymptotic distribution of the test statistic is normal and its Pitman asymptotic efficiency is as good as or higher than the competitors in the class of sub-sample Mann–Whitney–Wilcoxon statistics. [ABSTRACT FROM AUTHOR]

This paper considers statistical inference for a ranked set sample under a symmetry restriction on the underlying distribution. We present new estimators for the distribution function and the center of symmetry. It is shown that these estimators outperform their competitors in the literature. Based on the proposed distribution function estimator, a Kolmogorov–Smirnov type test is developed and the construction of a confidence interval is discussed. [Copyright &y& Elsevier]

This paper presents a ranked set sample allocation procedure that is optimal for a number of nonparametric test procedures. We define a function that measures the amount of information provided by each observation given the actual joint ranking of all the units in a set. The optimal ranked set sample allocates order statistics by maximizing this information function. This paper shows that the optimal allocation of order statistics in a ranked set sample is determined by the location of the mode(s) of the underlying distribution. For unimodal, symmetric distributions, optimal allocation always quantifies the middle observation(s). If the underlying distribution with cdf F is a multi-modal distribution with modes $R\_\{1\},\; \backslash ldots,\; R\_\{k\}$, then the optimal allocation procedure quantifies observations at $mF(R\_\{1\}),\; \backslash ldots,\; mF(R\_\{k\})$ in a set of size m. We provide similar results for unimodal, asymmetric distributions. We also propose a new sign test which considers the relative positions of the quantified observations from the same cycle in a ranked set sample. The proposed sign test provides improvement in the Pitman efficiency over the ranked set sample sign test of Hettmansperger (1995). It is shown that the information optimal allocation procedure induced by Pitman efficiency is equivalent to the optimal allocation procedure induced by the information criteria. We show that the finite sample distribution of the proposed test based on this optimal design is binomial. [ABSTRACT FROM AUTHOR]

We discuss two-armed clinical trials in which an ordinal response is observed on entry and at follow-up. In certain subject areas, such data are often reduced to the counts of patients who have deteriorated, remained the same, or improved. We develop asymptotic distribution theory to compare this approach to the use of nonparametric tests based on poststratification of the follow-up responses according to the entry levels. The theory for the latter approach is established by a general result for two-sample U statistics based on bivariate data. Application to data from clinical trials and evaluation of asymptotic relative efficiencies and powers for a variety of contexts illustrate the increased sensitivity of poststratified Wilcoxon tests. [ABSTRACT FROM AUTHOR]

Let X1,…,Xn be a sequence of independent and identically distributed random variables with an unknown underlying continuous cumulative distributive function F. Relative to this unknown distribution function, suppose one would like to test a null hypothesis concerning the goodness of fit of F to some distribution function using a Cramer-von Mises-type statistic. In some applications the null hypothesis is simple, whereas in others it may be composite. The subject of this article is the problem of comparing the efficiency of tests for the simple and composite hypotheses. Dyer (1974) abd Stephens (1974) noticed that for testing normality using the Cramer-von Mises statistic the test procedures for which the nuisnace parameters needed to be estimated were more powerful than the procedures in which the parameters were specified. We shall analytically compare these tests of the simple and composite hypotheses using the concepts of Bahadur efficiency and Pitman efficiency and thereby give a theoretical basis for the paradoxical simulation results of Dyer and Stephens. [ABSTRACT FROM AUTHOR]

This article examines the relative efficiency of finite induced and Wald-like (or "infinite induced") tests of some commonly encountered joint hypotheses. One two-sided testing problem and two types of two-sided testing problems concerning two parameters and normally distributed estimates are considered. The exact slopes of six test statistics are derived, and from these the Bahadur relative efficiency of tests based on any pair of the statistics can be easily computed. For the problems considered, Bahadur relative efficiency is equal to limiting Pitman efficiency, whereas Pitman relative efficiency coincides with exact finite sample relative efficiency. I present numerical results showing that Bahadur relative efficiency generally approximates Pitman efficiency rather poorly, although the patterns exhibited by these two efficiency criteria bear a reasonable similarity in most cases. [ABSTRACT FROM AUTHOR]

The influence curve introduced by Hampel (1968) is applied to goodness-of-fit statistics. The efficacy curve is then defined to be the square of the influence curve weighted by a constant that arises in the context of approximate Bahadur efficiency. For a number of goodness-of-fit statistics, the ratios of these curves are shown to be equal to asymptotic relative efficiencies in the Pitman sense when testing for point contamination. These efficacy curves graphically portray the sensitivities of certain goodness-of-fit statistics to minor perturbations in the assumed distribution. [ABSTRACT FROM AUTHOR]

The locally most powerful test is derived for the hypothesis that the regression coefficients are constant over time against the alternative that they vary according to the random walk process. When the regression equation contains the constant term only, comparisons are made with the tests suggested by LaMotte and McWhorter (1978). These are based on exact powers and on three different types of asymptotic efficiencies including the classical Pitman and Bahadur approaches and the new one due to Gregory (1980). The concept of the Bahadur efficiency is extended to cover also the random slopes. Suggestions are made for choosing the test. [ABSTRACT FROM AUTHOR]

A general class of nonparametric test statistics is constructed by considering the sign of the most extreme value in sub samples of size m taken from n independent observations. The test statistics can be expressed as linear rank statistics and reduce to the sign test statistic for m = 1 and a modified Wilcoxon signed-rank test statistic for m = 2. Asymptotic normality of properly standardized versions of our statistics is established under general 'conditions. Small sample power simulations as well as Pitman and Bahadur efficiencies indicate that members of our class do well in comparison with already existing test statistics. [ABSTRACT FROM AUTHOR]