A method for constructing exact tests from test statistics that have unknown null distributions

A randomized procedure is described for constructing an exact test from a test statistic F for which the null distribution is unknown. The procedure is restricted to cases where F is a function of a random element U that has a known distribution under the null hypothesis. The power of the exact randomized test is shown to be greater in some cases than the power of the exact nonrandomized test that could be constructed if the null distribution of Fwere known.     

Weighted Logrank Permutation Tests for Randomly Right Censored Life Science Data

In biomedical research, weighted logrank tests are frequently applied to compare two samples of randomly right censored survival times. We address the question how to combine a number of weighted logrank statistics to achieve good power of the corresponding survival test for a whole linear space or cone of alternatives, which are given by hazard rates. This leads to a new class of semiparametric projection tests that are motivated by likelihood ratio tests for an asymptotic model. We show that these tests can be carried out as permutation tests and discuss their asymptotic properties. A simulation study together with the analysis of a classical data set illustrates the advantages.     

A Diagnostic Test for Normality Within the Power Exponential Family

This article develops the locally uniformly most powerful unbiased Lagrange multiplier test of normality of regression disturbances within the family of power exponential distributions. The small sample power properties of the test are compared in a Monte Carlo study with 6 well-known tests across 12 alternative nonnormal distributions. In addition, the finite sample power properties for nonnormal alternatives within the power exponential family are summarized by estimating response surfaces. The results suggest that the proposed text is computationally convenient and possesses relatively attractive power properties even against alternatives outside the power exponential family.     

Bayesian Network Structure Learning with Permutation Tests

In literature there are several studies on the performance of Bayesian network structure learning algorithms. The focus of these studies is almost always the heuristics the learning algorithms are based on, i.e., the maximization algorithms (in score-based algorithms) or the techniques for learning the dependencies of each variable (in constraint-based algorithms). In this article, we investigate how the use of permutation tests instead of parametric ones affects the performance of Bayesian network structure learning from discrete data. Shrinkage tests are also covered to provide a broad overview of the techniques developed in current literature.     

The measurement of capital utilisation rates

A strategy using spline function interpolation is developed f o r estimating capital utilisation rates . Cobb-Douglas, CES and translog functional forms are used in estimation. Tests for functional forms are conducted leading t o t h e s e l e c t i o n of the Cobb-Douglas form. Quarterly series of estimated utilisation rates and excess capacity measures are presented.     

On the Relationship between Directional and Omnibus Statistical Tests

Abstract.  A common statistical problem involves the testing of a K -dimensional parameter vector. In both parametric and semiparametric settings, two types of directional tests – linear combination and constrained tests – are frequently used instead of omnibus tests in hopes of achieving greater power for specific alternatives. In this paper, we consider the relationship between these directional tests, as well as their relationship to omnibus tests. Every constrained directional test is shown to be asymptotically equivalent to a specific linear combination test under a sequence of contiguous alternatives and vice versa. Even when the direction of the alternative is known, the constrained test in general will not be optimal unless the objective function used to derive it is efficient. For an arbitrary alternative, insight into the power characteristics of directional tests in comparison to omnibus tests can be gained by a chi-square partition of the omnibus test.     

Union-Intersection testing for outliers in multivariate normal data

The union-intersection approach to multivariate test construction is used to develop an alternative to Wilks' likelihood ratio test statistic for testing for two or more outliers in multivariate normal data. It is shown that critical values of both statistics are poorly approximated by Bonferroni bounds. Simulated critical values are presented for both statistics for significance levels 1% and 5%, for sample sizes 10(5)30, 40, 50, 75 and 100 for 2, 3, 4 and 5 dimensions. A power comparison of the two tests in the slippage of the mean model for generating outliers indicates that the union-intersection test is the more powerful when the slippages are close to collinear. Although Wilks' test remains the preference for general use, the union-intersection test could be valuable when such special structure in the data is suspected.     

A survey of permutation tests for censored survival data

The present paper surveys tests with censored sur-vival data for 2-and k-samples and for association by a framework which classifies them into complete or restric-ted permutation tests and into tests based on U-or Savage-scores. The formulae of the resulting twelve tests are briefly described for quick reference. Some of the tests have been applied frequently in the past as the tests by Mantel, Breslow or Gehan; others have been developed rather recently, partly by the author. The concluding discussion presents the results of a simulation study, clarifying similarities and differences of the restricted and complete permutation approach, and deals with rela-tive efficiencies of the two scoring systems.     

Permuiation tesis for k-sample binomial data with comparisons of exact and approximate P-levels

Exact ksample permutation tests for binary data for three commonly encountered hypotheses tests are presented,, The tests are derived both under the population and randomization models . The generating function for the number of cases in the null distribution is obtained, The asymptotic distributions of the test statistics are derived . Actual significance levels are computed for the asymptotic test versions , Random sampling of the null distribution is suggested as a superior alternative to the asymptotics and an efficient computer technique for implementing the random sampling is described., finally, some numerical examples are presented and sample size guidelines given for computer implementation of the exact tests.     

THE POWER OF STUDENT'S t TEST: CAN A NON-SIMILAR TEST DO BETTER?

Lehmann & Stein (1948) proved the existence of non-similar tests which can be more powerful than best similar tests. They used Student's problem of testing for a non-zero mean given a random sample from the normal distribution with unknown variance as an example. This raises the question: should we use a non-similar test instead of Student's t test? Questions like this can be answered by comparing the power of the test with the power envelope. This paper discusses the difficulties involved in computing power envelopes. It reports an empirical comparison of the power of the t test and the power envelope and finds that the two are almost identical especially for sample sizes greater than 20. These findings suggest that, as well as being uniformly most powerful (UMP) within the class of similar tests, Student's t test is approximately UMP within the class of all tests. For practical purposes it might also be regarded as UMP when moderate or large sample sizes are involved.     

Assessing the fit of finite mixture distributions

Mixture distributions have become a very flexible and common class of distributions, used in many different applications, but hardly any literature can be found on tests for assessing their goodness of fit. We propose two types of smooth tests of goodness of fit for mixture distributions. The first test is a genuine smooth test, and the second test makes explicit use of the mixture structure. In a simulation study the tests are compared to some traditional goodness of fit tests that, however, are not customised for mixture distributions. The first smooth test has overall good power and generally outperforms the other tests. The second smooth test is particularly suitable for assessing the fit of each component distribution separately. The tests are applicable to both continuous and discrete distributions and they are illustrated on three medical data sets.     

Tables of the cramér-von mises distributions

Tables of the one- and two-sample unweighted Cramer-von Mises statistics are given, and compared with the limiting distribution. The two-sample statistic may be useful in (for example) clinical trials when a proportional hazards assumption (which leads to the use of the log-rank test) is unjustified: see, for example, Schumacher (1984). It is often possible to stop clinical trials early if the Cramer-von Mises test (rather than say, the log-rank test) is employed.     

Exact Multivariate Permutation Tests for Fixed Effects in Mixed-Models

A test for the fixed effect in mixed-models is proposed. It is based on permutation strategy and is exact. The testing approach presented is very general and the class of models covered is very broad.

Multivariate responses with different type of variables (e.g., continuous, categorical, and ranks) are usually tested with separated models and the overall test are usually reached through Bonferroni-like combinations, i.e., without taking into account the joint distribution of the test statistics. On the contrary, in this approach the joint distribution is immediately obtained and the dependence among tests is taken into account in the overall test. The methods are implemented in the R package flip, freely available on CRAN.     

The Performance of Randomization Tests that Use Permutations of Independent Variables

ABSTRACT

In this article we evaluate the performance of a randomization test for a subset of regression coefficients in a linear model. This randomization test is based on random permutations of the independent variables. It is shown that the method maintains its level of significance, except for extreme situations, and has power that approximates the power of another randomization test, which is based on the permutation of residuals from the reduced model. We also show, via an example, that the method of permuting independent variables is more valuable than other randomization methods because it can be used in connection with the downweighting of outliers.     

Deriving a lower bound for the proportion of perceivers in replicated difference tests by means of multiple test theory

Analyzing repeated difference tests aims in significance testing for differences as well as in estimating the mean discrimination ability of the consumers. In addition to the average success probability, the proportion of consumers that may detect the difference between two products and therefore account for any increase of this probability is of interest. While some authors address the first two goals, for the latter one only an estimator directly linked to the average probability seems to be used. However, this may lead to unreasonable results. Therefore we propose a new approach based on multiple test theory. We define a suitable set of hypotheses that is closed under intersection. From this, we derive a series of hypotheses that may be sequentially tested while the overall significance level will not be violated. By means of this procedure we may determine a minimal number of assessors that must have perceived the difference between the products at least once in a while. From this, we can find a conservative lower bound for the proportion of perceivers within the consumers. In several examples, we give some insight into the properties of this new method and show that the knowledge about this lower bound might indeed be valuable for the investigator. Finally, an adaption of this approach for similarity tests will be proposed.     

A re-appraisal of tests for normality

Tests for normality can be divided into two groups - those based upon a function of the empirical distribution function and those based upon a function of the original observations. The latter group of statistics test spherical symmetry and not necessarily normality. If the distribution is completely specified then the first group can be used to test for ‘spherical’ normality. However, if the distribution is incompletely specified and F‘‘x_i - x’/s’ is used these test statistics also test sphericity rather than normality. A Monte Carlo study was conducted for the completely specified case, to investigate the sensitivity of the distance tests to departures from normality when the alternative distributions are non-normal spherically symmetric laws. A “new” test statistic is proposed for testing a completely specified normal distribution     

Nonparametric tests for multivariate multi-sample locations based on data depth

Several nonparametric tests for multivariate multi-sample location problem are proposed in this paper. These tests are based on the notion of data depth, which is used to measure the centrality/outlyingness of a given point with respect to a given distribution or a data cloud. Proposed tests are completely nonparametric and implemented through the idea of permutation tests. Performance of the proposed tests is compared with existing parametric test and nonparametric test based on data depth. An extensive simulation study reveals that proposed tests are superior to the existing tests based on data depth with regard to power. Illustrations with real data are provided.     

A Nonparametric Test for Autoregressive Conditional Heteroscedasticity: A Markov-Chain Approach

In this article we propose a nonparametric test for autoregressive conditional heteroscedasticity based on finite-state Markov chains. A simple Monte Carlo experiment suggests that in finite samples it performs comparably to the Lagrange multiplier test under conditional normality and is superior for the t, lognormal, and exponential distributions. As an illustration, we apply both tests to Canadian/U.S. forward foreign exchange data.     

Conditional Studentized Survival Tests for Randomly Censored Models

It is shown that in the case of heterogenous censoring distributions Studentized survival tests can be carried out as conditional permutation tests given the order statistics and their censoring status. The result is based on a conditional central limit theorem for permutation statistics. It holds for linear test statistics as well as for sup-statistics. The procedure works under one of the following general circumstances for the two-sample problem: the unbalanced sample size case, highly censored data, certain non-convergent weight functions or under alternatives. For instance, the two-sample log rank test can be carried out asymptotically as a conditional test if the relative amount of uncensored observations vanishes asymptotically as long as the number of uncensored observations becomes infinite. Similar results hold whenever the sample sizes and are unbalanced in the sense that and hold.     

Testing for serial correlation in the presence of dynamic heteroscedasticity

Standard serial correlation tests are derived assuming that the disturbances are homoscedastic, but this study shows that asympotic critical values are not accurate when this assumption is violated. Asymptotic critical values for the ARCH(2)-corrected LM, BP and BL tests are valid only when the underlying ARCH process is strictly stationary, whereas Wooldridge's robust LM test has good properties overall. These tests exhibit similar bahaviour even when the underlying process is GARCH (1,1). When the regressors include lagged dependent variables, the rejection frequencies under both the null and alternative hypotheses depend on the coefficientsof the lagged dependent variables and the other model parameters. They appear to be robust across various disturbance distributions under the null hypothesis.