A nonparametric repeated significance test with adaptive target sample size

In this article a general result is derived that, along with a functional central limit theorem for a sequence of statistics, can be employed in developing a nonparametric repeated significance test with adaptive target sample size. This method is used in deriving a repeated significance test with adaptive target sample size for the shift model. The repeated significance test is based on a functional central limit theorem for a sequence of partial sums of truncated observations. Based on numerical results presented in this article one can conclude that this nonparametric sequential test performs quite well.     

Testing for Homogeneity in Mixture Using Weighted Relative Entropy

In this article, we propose a test for homogeneity based on Kullback–Leibler information (also known as relative entropy). Though widely used in hypothesis testing problems, Kullback–Leibler information is not desirable to many researchers in the context of mixture because of its complicated form. In this article, a weighted relative entropy test (WE test), which has closed form expression in terms of the parameter estimators, is proposed. Theoretical results show that this test is consistent. Some simulation results demonstrate that the WE test is better than some leading tests when the mixture components come from normal distribution, and is competitive with them in the Poisson case. The usage of the test is illustrated in an example with data about acidity index of lakes.     

A Unified Approach to Likelihood Inference on Linear Inequality Constraints in Contingency Tables

In contingency table analysis, a likelihood ratio test for linear inequality constraints is discussed. The restriction condition considered in this article is much more general than usual stochastic order restriction conditions. Asymptotic property of test statistic is shown. Simulation study is conducted to compare the empirical power and size performed via the proposed method and others. Several real data sets are used to illustrate our theoretical result. The idea used in this article can be applied to test the problems with nonlinear inequality constraints.     

Stratified Logrank Test of No Randomized Treatment Effect with Missing Stratum Information

A major objective in many clinical trials is to compare several competing treatments in a randomized experiment. In such studies, it is often necessary to adjust for some other important factor that affects the event rates in the treatment groups. When this factor is discrete, one usual approach uses a stratified version of the logrank test. In this article, we consider the problem that arises when the factor giving rise to the strata is missing at random for some of the study subjects. This article proposes a modified version of the stratified logrank test, in which the unobserved stratum indicators are replaced by an estimate of their conditional expectation given available auxiliary covariate measurements. The null asymptotic distribution of the proposed test statistic is investigated. Simulation experiments are also conducted to examine the finite-sample behavior of this test under both null and alternative hypotheses. Simulations indicate that the proposed test performs well, even under some moderate deviations to the at-random missingness assumption.     

A Necessary Power Divergence Type Family Tests of Multivariate Normality

In a recent article, Cardoso de Oliveira and Ferreira have proposed a multivariate extension of the univariate chi-squared normality test, using a known result for the distribution of quadratic forms in normal variables. In this article, we propose a family of power divergence type test statistics for testing the hypothesis of multinormality. The proposed family of test statistics includes as a particular case the test proposed by Cardoso de Oliveira and Ferreira. We assess the performance of the new family of test statistics by using Monte Carlo simulation. In this context, the type I error rates and the power of the tests are studied, for important family members. Moreover, the performance of significant members of the proposed test statistics are compared with the respective performance of a multivariate normality test, proposed recently by Batsidis and Zografos. Finally, two well-known data sets are used to illustrate the method developed in this article as well as the specialized test of multivariate normality proposed by Batsidis and Zografos.     

Testing for Serial Independence: Beyond the Portmanteau Approach

Portmanteau tests are typically used to test serial independence even if, by construction, they are generally powerful only in presence of pairwise dependence between lagged variables. In this article, we present a simple statistic defining a new serial independence test, which is able to detect more general forms of dependence. In particular, differently from the Portmanteau tests, the resulting test is powerful also under a dependent process characterized by pairwise independence. A diagram, based on p-values from the proposed test, is introduced to investigate serial dependence. Finally, the effectiveness of the proposal is evaluated in a simulation study and with an application on financial data. Both show that the new test, used in synergy with the existing ones, helps in the identification of the true data-generating process. Supplementary materials for this article are available online.     

Modified Wilcoxon–Mann–Whitney Test and Power Against Strong Null

The Wilcoxon–Mann–Whitney (WMW) test is a popular rank-based two-sample testing procedure for the strong null hypothesis that the two samples come from the same distribution. A modified WMW test, the Fligner–Policello (FP) test, has been proposed for comparing the medians of two populations. A fact that may be under-appreciated among some practitioners is that the FP test can also be used to test the strong null like the WMW. In this article, we compare the power of the WMW and FP tests for testing the strong null. Our results show that neither test is uniformly better than the other and that there can be substantial differences in power between the two choices. We propose a new, modified WMW test that combines the WMW and FP tests. Monte Carlo studies show that the combined test has good power compared to either the WMW and FP test. We provide a fast implementation of the proposed test in an open-source software. Supplementary materials for this article are available online.     

Linear Signed Rank Test for Model Selection

In this article, we consider a linear signed rank test for non-nested distributions in the context of the model selection. Introducing a new test, we show that, it is asymptotically more efficient than the Vuong test and the test statistic based on B statistic introduced by Clarke. However, here, we let the magnitude of the data give a better performance to the test statistic. We have shown that this test is an unbiased one. The results of simulations show that the rank test has the greater statistical power than the Vuong test where the underline distributions is symmetric.     

TESTS FOR EXPONENTIALITY AGAINST GAMMA ALTERNATIVES USING NORMALIZED WAITING TIMES

In this article, we present some tests for Exponentiality against Gamma alternatives by using normalized waiting times. The test is constructed by using a quadratic form. The asymptotic distribution of the proposed test is derived. The power of the test is computed through Monte Carlo simulation and is compared with Linhart (1965) test, Bain and Engelhardt (1975) test and Keating et al. (1990) test.     

A test for gamma DFR alternative

In this article, a test for exponentiality against gamma DFR alternative based on a quadratic form of the logarithmic observations is proposed. The percentage points and the power of the test are computed through Monte-Carlo simulation. The test is seen to perform well as compared to a chi-square test proposed by Bain and Engelhardt(1975).     

Nearly optimal truncated group sequential test on binomial proportions

In this article, we systematically study the optimal truncated group sequential test on binomial proportions. Through analysis of the cost structure, average test cost is introduced as a new optimality criterion. According to the new criterion, the optimal tests on different design parameters including the boundaries, success discriminant value, stage sample vector, stage size, and the maximum sample size are defined. Since the computation time in finding optimal designs by exhaustive search is intolerably long, group sequential sample space sorting method and procedures are developed to find the near-optimal ones. In comparison with the international standard ISO2859-1, the truncated group sequential designs proposed in this article can reduce the average test costs around 20%.     

More Powerful Tests from Confidence Interval p Values

In this article the problem of comparing two independent binomial populations is considered. It is shown that the test based on the confidence interval p value of Berger and Boos often is uniformly more powerful than the standard unconditional test. This test also requires less computational time.     

Entropy-based goodness-of-fit tests for the Pareto I distribution

In this article, having observed the generalized order statistics in a sample, we construct a test for the hypothesis that the underlying distribution is the Pareto I distribution. The Shannon entropy of generalized order statistics is used to test the null hypothesis.     

Testing Alphas in Conditional Time-Varying Factor Models With High-Dimensional Assets

ABSTRACT

For conditional time-varying factor models with high-dimensional assets, this article proposes a high-dimensional alpha (HDA) test to assess whether there exist abnormal returns on securities (or portfolios) over the theoretical expected returns. To employ this test effectively, a constant coefficient test is also introduced. It examines the validity of constant alphas and factor loadings. Simulation studies and an empirical example are presented to illustrate the finite sample performance and the usefulness of the proposed tests. Using the HDA test, the empirical example demonstrates that the FF three-factor model is better than CAPM in explaining the mean-variance efficiency of both the Chinese and U.S. stock markets. Furthermore, our results suggest that the U.S. stock market is more efficient in terms of mean-variance efficiency than the Chinese stock market. Supplementary materials for this article are available online.     

Maximum Average-Power (MAP) Tests

The objective of this article is to propose and study frequentist tests that have maximum average power, averaging with respect to some specified weight function. First, some relationships between these tests, called maximum average-power (MAP) tests, and most powerful or uniformly most powerful tests are presented. Second, the existence of a maximum average-power test for any hypothesis testing problem is shown. Third, an MAP test for any hypothesis testing problem with a simple null hypothesis is constructed, including some interesting classical examples. Fourth, an MAP test for a hypothesis testing problem with a composite null hypothesis is discussed. From any one-parameter exponential family, a commonly used UMPU test is shown to be also an MAP test with respect to a rich class of weight functions. Finally, some remarks are given to conclude the article.     

Optimal progressive group-censoring plans for exponential distribution in presence of cost constraint

This article discusses a life test under progressive type-I group-censoring. We use maximum likelihood method to obtain the point and interval estimators of the parameter of lifetime distribution. In order to obtain a precise estimate of mean life, one needs to design an optimal life test. Thus, this article proposes an approach to determine the number of test units, number of inspections, and length of inspection interval of a life test under a pre-determined budget of experiment such that the asymptotic variance of estimator of mean life is minimum. The method will be applied to two numerical examples and the sensitivity analysis will be investigated.     

Testing Serial Correlation in Partial Linear Errors-in-Variables Models Based on Empirical Likelihood

In this article, we propose an empirical likelihood-based test to check the existence of serial correlation in partial linear errors-in-variables models. A nonparametric version of Wilk' theorem is derived, which says that our proposed test has an asymptotic chi-square distribution. Simulation results reveal that the finite sample performance of our proposed test is satisfactory in both size and power.     

Empirical Likelihood-based Inference for Stationary-ergodicity of the Generalized Random Coefficient Autoregressive Model

In this article, we consider the application of the empirical likelihood method to the generalized random coefficient autoregressive (GRCA) model. When the order of the model is 1, we derive an empirical likelihood ratio test statistic to test the stationary-ergodicity. Some simulation studies are also conducted to investigate the finite sample performances of the proposed test.     

A New Goodness-of-Fit Test Based on the Empirical Characteristic Function

In this article, we present a goodness-of-fit test for a distribution based on some comparisons between the empirical characteristic function c_n(t) and the characteristic function of a random variable under the simple null hypothesis, c₀(t). We do this by introducing a suitable distance measure. Empirical critical values for the new test statistic for testing normality are computed. In addition, the new test is compared via simulation to other omnibus tests for normality and it is shown that this new test is more powerful than others.     

An Improvement of the Nonparametric Bootstrap Test for the Comparison of the Coefficient of Variations

In this article, we propose a new test for examining the equality of the coefficient of variation between two different populations. The proposed test is based on the nonparametric bootstrap method. It appears to yield several appreciable advantages over the current tests. The quick and easy implementation of the test can be considered as advantages of the proposed test. The test is examined by the Monte Carlo simulations, and also evaluated using various numerical studies.