Robust test for independence in high dimensions

This article develops a new test based on Spearman’s rank correlation coefficients for total independence in high dimensions. The test is robust to the non normality and heavy tails of the data, which is a merit that is not shared by the existing tests in literature. Simulation results suggest that the new test performs well under several typical null and alternative hypotheses. Besides, we employ a real data set to illustrate the use of the new test.     

A joint test for parametric specification and independence in nonlinear regression models

This paper develops a testing procedure to simultaneously check (i) the independence between the error and the regressor(s), and (ii) the parametric specification in nonlinear regression models. This procedure generalizes the existing work of Sen and Sen [“Testing Independence and Goodness-of-fit in Linear Models,” Biometrika, 101, 927–942.] to a regression setting that allows any smooth parametric form of the regression function. We establish asymptotic theory for the test procedure under both conditional homoscedastic error and heteroscedastic error. The derived tests are easily implementable, asymptotically normal, and consistent against a large class of fixed alternatives. Besides, the local power performance is investigated. To calibrate the finite sample distribution of the test statistics, a smooth bootstrap procedure is proposed and found work well in simulation studies. Finally, two real data examples are analyzed to illustrate the practical merit of our proposed tests.     

Evaluating the power of the mann-whitney test using the bootstrap method

In this paper we evaluate the power of the Mann-Whitney test in the shift model G(x) = F (x+θ) for all x , where the distribution of G is obtained by shifting F by an amount of θ.

The bootstrap method was used to evaluate the power of the Mann-Whitney test . A comparison among the bootstrap power , the asymptotic power of the Mann-Whitney test and the t-test power proved that the bootstrap is a better technique , because , it does not require the assumption of normality.     

An entropy test for the Rayleigh distribution and power comparison

In this paper, a goodness-of-fit test is proposed for the Rayleigh distribution. This test is based on the Kullback–Leibler discrimination methodology proposed by Song [2002, Goodness of fit tests based on Kullback–Leibler discrimination, IEEE Trans. Inf. Theory 48(5), pp. 1103–1117]. The critical values and powers for some alternatives are obtained by simulation. The proposed test is compared with other tests, namely Kolmogorov–Smirnov, Kuiper, Cramer–von Mises, Watson and Anderson–Darling. The use of the proposed test is shown in a real example.     

On entropy-based goodness-of-fit test for asymmetric Student-t and exponential power distributions

This paper examines the goodness-of-fit (GOF) test for a generalized asymmetric Student-t distribution (ASTD) and asymmetric exponential power distribution (AEPD). These distributions are known to include a broad class of distribution families and are quite suitable to modelling the innovations of financial time series. Despite their popularity, to our knowledge, no studies in the literature have so far investigated their affinity and differences in implementation. To fill this gap, we examine the empirical power behaviour of entropy-based GOF tests for hypotheses wherein the ASTD and AEPD play the role of null and alternative distributions. Our findings through a simulation study and real data analysis indicate that the two distributions are generally hard to distinguish and that the ASTD family accommodates AEPDs to a greater degree than the other way around for larger samples.     

A simple test procedure in standardizing the power of Hosmer–Lemeshow test in large data sets

The Hosmer–Lemeshow (H–L) test is a widely used method when assessing the goodness-of-fit of a logistic regression model. However, the H–L test is sensitive to the sample sizes and the number of groups in H–L test. Cautions need to be taken for interpreting an H–L test with a large sample size. In this paper, we propose a simple test procedure to evaluate the model fit of logistic regression model with a large sample size, in which a bootstrap method is used and the test result is determined by the power of H–L test at the target sample size. Simulation studies show that the proposed method can effectively standardize the power of the H–L test under the pre-specified level of type I error. Application to the two datasets illustrates the usefulness of the proposed model.     

A modified chi-square test of independence against a class of ordered alternatives in an r x c contingency table

A modified chi-square test statistic is constructed for testing the hypothesis of independence in a two-way contingency table against a class of ordered alternatives defined in terms of pooled cross-product ratios. The test procedure can also be used to test for positive quadrant dependence in a two-way contingency table. The asymptotic distribution of the test statistic under the null hypothesis is obtained. Some power comparisons with known test procedures are given. A numerical example is given to illustrate the use of this test.     

Computation of the percentage points and the power for the two-sided Kolmogorov-Smirnov one sample test

Two recursive schemes are presented for the calculation of the probabilityP(g(x)≤S _n (x)≤h(x) for allx∈®), whereS _n is the empirical distribution function of a sample from a continuous distribution andh, g are continuous and isotone functions. The results are specialized for the calculation of the distribution and the corresponding percentage points of the test statistic of the two-sided Kolmogorov-Smirnov one sample test. The schemes allow the calculation of the power of the test too. Finally an extensive tabulation of percentage points for the Kolmogorov-Smirnov test is given.     

Comparison of ANOVA-F and ANOM tests with regard to type I error rate and test power

A Monte Carlo simulation was conducted to compare the type I error rate and test power of the analysis of means (ANOM) test to the one-way analysis of variance F-test (ANOVA-F). Simulation results showed that as long as the homogeneity of the variance assumption was satisfied, regardless of the shape of the distribution, number of group and the combination of observations, both ANOVA-F and ANOM test have displayed similar type I error rates. However, both tests have been negatively affected from the heterogeneity of the variances. This case became more obvious when the variance ratios increased. The test power values of both tests changed with respect to the effect size (Δ), variance ratio and sample size combinations. As long as the variances are homogeneous, ANOVA-F and ANOM test have similar powers except unbalanced cases. Under unbalanced conditions, the ANOVA-F was observed to be powerful than the ANOM-test. On the other hand, an increase in total number of observations caused the power values of ANOVA-F and ANOM test approach to each other. The relations between effect size (Δ) and the variance ratios affected the test power, especially when the sample sizes are not equal. As ANOVA-F has become to be superior in some of the experimental conditions being considered, ANOM is superior in the others. However, generally, when the populations with large mean have larger variances as well, ANOM test has been seen to be superior. On the other hand, when the populations with large mean have small variances, generally, ANOVA-F has observed to be superior. The situation became clearer when the number of the groups is 4 or 5.     

Maximum likelihood estimation of correlation between maximal oxygen consumption and the 6-min walk test in patients with chronic heart failure

Maximal oxygen consumption (VO₂max) is the standard measurement used to quantify cardiovascular functional capacity and aerobic fitness. Unfortunately, it is a costly, impractical and labour-intensive measure to obtain. The 6-min walk test (6MWT) also assesses cardiopulmonary function, but in contrast to the VO₂max test, it is inexpensive and can be performed almost anywhere. Various medical studies have addressed the correlation between VO₂max and 6MWT in patients with chronic heart failure. Of particular interest, from a medical point of view, is the conditional correlation between the two measures given the individual's height, weight, age and gender. In this paper, we have calculated the maximum likelihood estimate of the conditional correlation in patients with chronic heart failure under the assumption of skew normality. Data were recorded from 98 patients in the Operative Unit of Thoracic Surgery in Bari, Italy. The estimated conditional correlation was found to be much smaller than estimated marginal correlations reported in the medical literature.     

Evaluating the power of Minitab's data subsetting lack of fit test in multiple linear regression

Minitab's data subsetting lack of fit test (denoted XLOF) is a combination of Burn and Ryan's test and Utts' test for testing lack of fit in linear regression models. As an alternative to the classical or pure error lack of fit test, it does not require replicates of predictor variables. However, due to the uncertainty about its performance, XLOF still remains unfamiliar to regression users while the well-known classical lack of fit test is not applicable to regression data without replicates. So far this procedure has not been mentioned in any textbooks and has not been included in any other software packages. This study assesses the performance of XLOF in detecting lack of fit in linear regressions without replicates by comparing the power with the classic test. The power of XLOF is simulated using Minitab macros for variables with several forms of curvature. These comparisons lead to pragmatic suggestions on the use of XLOF. The performance of XLOF was shown to be superior to the classical test based on the results. It should be noted that the replicates required for the classical test made itself unavailable for most of the regression data while XLOF can still be as powerful as the classic test even without replicates.     

Revisiting purchasing power parity in BRICS countries using more powerful quantile unit-root tests with stationary covariates

This study contributes to this line of research by determining whether purchasing power parity (PPP) holds true in BRICS countries (i.e., Brazil, Russia, India, China, and South Africa). We test the hypothesis of PPP in real exchange rate using a more powerful quantile unit-root test with stationary covariates. Our empirical findings indicate a support of PPP for all BRICS countries under study. Our study has important policy implications for the government of the BRICS countries conducting exchange rate policy through PPP.     

Improving precision and power in randomized trials with a two-stage study design: Stratification using clustering method

In a randomized controlled trial (RCT), it is possible to improve precision and power and reduce sample size by appropriately adjusting for baseline covariates. There are multiple statistical methods to adjust for prognostic baseline covariates, such as an ANCOVA method. In this paper, we propose a clustering-based stratification method for adjusting for the prognostic baseline covariates. Clusters (strata) are formed only based on prognostic baseline covariates, not outcome data nor treatment assignment. Therefore, the clustering procedure can be completed prior to the availability of outcome data. The treatment effect is estimated in each cluster, and the overall treatment effect is derived by combining all cluster-specific treatment effect estimates. The proposed implementation of the procedure is described. Simulations studies and an example are presented.     

Exact calculation of power and sample size in bioequivalence studies using two one‐sided tests

The number of subjects in a pharmacokinetic two‐period two‐treatment crossover bioequivalence study is typically small, most often less than 60. The most common approach to testing for bioequivalence is the two one‐sided tests procedure. No explicit mathematical formula for the power function in the context of the two one‐sided tests procedure exists in the statistical literature, although the exact power based on Owen's special case of bivariate noncentral t‐distribution has been tabulated and graphed. Several approximations have previously been published for the probability of rejection in the two one‐sided tests procedure for crossover bioequivalence studies. These approximations and associated sample size formulas are reviewed in this article and compared for various parameter combinations with exact power formulas derived here, which are computed analytically as univariate integrals and which have been validated by Monte Carlo simulations. The exact formulas for power and sample size are shown to improve markedly in realistic parameter settings over the previous approximations. Copyright © 2014 John Wiley & Sons, Ltd.