A new two-sample test for choosing between log-rank and Wilcoxon tests with right-censored data

When differences of survival functions are located in early time, a Wilcoxon test is the best test, but when differences of survival functions are located in late time, using a log-rank test is better. Therefore, a researcher needs a stable test in these situations. In this paper, a new two-sample test is proposed and considered. This test is distribution-free. This test is useful for choosing between log-rank and Wilcoxon tests. Its power is roughly the maximal power of the log-rank test and Wilcoxon test.     

Locally best tests for exponential distributions with interval-censored data

In this article, we derive a locally best test for testing the mean of exponential distributions with interval-censored samples. This locally best test possesses certain optimality. It is of unbiasedness and equivalent to a likelihood ratio test in some circumstances, and it is also a Bayes test for some loss function. For the locally best test, the associated critical values and powers at a nominal level of significance are provided. For a large sample size case, asymptotic critical values and powers are also calculated and tabulated. Moreover, based on the locally best test, a curtailed test is proposed. This curtailed test is equivalent to the locally best test on the acceptance or rejection of the null hypothesis. A Monte Carlo simulation is carried out to illustrate the performance of the curtailed test compared with the locally best test. Numerical results show that the experimental duration time of the curtailed test is substantially smaller than that of the locally best test.     

Maximum Test versus Adaptive Tests for the Two-Sample Location Problem

For the non-parametric two-sample location problem, adaptive tests based on a selector statistic are compared with a maximum and a sum test, respectively. When the class of all continuous distributions is not restricted, the sum test is not a robust test, i.e. it does not have a relatively high power across the different possible distributions. However, according to our simulation results, the adaptive tests as well as the maximum test are robust. For a small sample size, the maximum test is preferable, whereas for a large sample size the comparison between the adaptive tests and the maximum test does not show a clear winner. Consequently, one may argue in favour of the maximum test since it is a useful test for all sample sizes. Furthermore, it does not need a selector and the specification of which test is to be performed for which values of the selector. When the family of possible distributions is restricted, the maximin efficiency robust test may be a further robust alternative. However, for the family of t distributions this test is not as powerful as the corresponding maximum test.     

The limit test statistic distribution of the maximum value test for right-censored data

ABSTRACT

In this paper, the maximum value test is proposed and considered for two-sample problem solving with lifetime data. This test is a distribution-free test under non-censoring and is a not distribution-free test under censoring. The formula of the limit distribution of the proposed maximal value test is represented in the general case. The distribution of the test statistic has been studied experimentally. Also, we propose the estimate of a p-value calculation of the maximum value test instead of the Monte-Carlo simulation. This test is useful and applicable in case of choosing among the logrank test, the Cox–Mantel test, the Q test and Generalized Wilcoxon tests, for instance, the Gehan's Generalized Wilcoxon test and the Peto and Peto's Generalized Wilcoxon test.     

An exact test for trend among binomial proportions based on a modified Baumgartner-Weiß-Schindler statistic

The Cochran-Armitage test is the most frequently used test for trend among binomial proportions. This test can be performed based on the asymptotic normality of its test statistic or based on an exact null distribution. As an alternative, a recently introduced modification of the Baumgartner-Weiß-Schindler statistic, a novel nonparametric statistic, can be used. Simulation results indicate that the exact test based on this modification is preferable to the Cochran-Armitage test. This exact test is less conservative and more powerful than the exact Cochran-Armitage test. The power comparison to the asymptotic Cochran-Armitage test does not show a clear winner, but the difference in power is usually small. The exact test based on the modification is recommended here because, in contrast to the asymptotic Cochran-Armitage test, it guarantees a type I error rate less than or equal to the significance level. Moreover, an exact test is often more appropriate than an asymptotic test because randomization rather than random sampling is the norm, for example in biomedical research. The methods are illustrated with an example data set.     

Homogeneity testing in a Weibull mixture model

The mixed Weibull distribution provides a flexible model to analyze random durations in a possibly heterogeneous population. To test for homogeneity against unobserved heterogeneity in a Weibull mixture model, a dispersion score test and a goodness-of-fit test are investigated. The empirical power of these tests is assessed and compared on a broad range of alternatives. It comes out that the dispersion score test, as it is based on a Weibull-to-exponential transformation, often breaks down. A simple new procedure is introduced for Weibull mixtures in scale, which combines the dispersion score test and the goodness-of-fit test. The new test is compared with several known procedures and shown to have a good overall power. To detect mixtures in shape and scale, a goodness-of-fit test is recommended. This research has been partially sponsored by a grant of the Deutsche Forschungsgemeinschaft. We thank Lars Haferkamp for computational assistance and Wilfried Seidel and a referee for their remarks on alternative test procedures.     

A sequential testing procedure for outliers and structural change

In this paper a test for outliers based on externally studentized residuals is shown to be related to a test for predictive failure. The relationships between a test for outliers, a test for a correlated mean shift and a test for an intercept shift are developed. A sequential testing procedure for outliers and structural change is shown to be independent, so that the overall size of the joint test can be determined exactly. It is established that a joint test for outliers and constancy of variances cannot be performed.     

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.     

Adaptive positive and negative runs test

As a nonparametric randomness test, the positive and negative runs test is widely used in practice due to the simplicity of its procedures. The test can lose efficiency if the alternative distribution is symmetrical at 0.5. In addition, the test can only be applied to test the randomness of a sequence from the uniform distribution. In this paper, we introduce an adaptive positive and negative runs test method to maximize the power function by choosing the optimal cut point. Also, the test is extended to check the randomness of a sequence generated from any other given distributions. Furthermore, we derive the exact distribution and obtain the asymptotical critical values of the proposed test statistics. Compared with the existed test, the efficiency of the proposed adaptive positive and negative runs test is competitive through simulation study.     

The rank von neumann test as a test for autocorrelation in regression models

The rank Von Neumann test, which performs extremely well as a test for serial correlation in raw data, is here compared with the Durbin-Watson and Geary tests as a test for autocorrelation in regression residuals. The test convincingly outperforms the Geary test but it is less robust than the Durbin-Watson test     

Testing a linear relationship in varying coefficient spatial autoregressive models

In this article, we propose a test to check a linear relationship in varying coefficient spatial autoregressive models, in which a residual-based bootstrap procedure is suggested to approximate the null distribution of the resulting test statistic. We conduct simulation studies to assess the performance of the test, including the validity of the bootstrap approximation to the null distribution of the test statistic and the power of the test. The simulation results demonstrate that the residual-based bootstrap procedure gives very accurate estimate of the null distribution of the test statistic and the test is of satisfactory power. Furthermore, a real example is given to demonstrate the application of the proposed test.     

A pooled Bayes test of independence for sparse contingency tables from small areas

We study the association between bone mineral density (BMD) and body mass index (BMI) when contingency tables are constructed from the several U.S. counties, where BMD has three levels (normal, osteopenia and osteoporosis) and BMI has four levels (underweight, normal, overweight and obese). We use the Bayes factor (posterior odds divided by prior odds or equivalently the ratio of the marginal likelihoods) to construct the new test. Like the chi-squared test and Fisher's exact test, we have a direct Bayes test which is a standard test using data from each county. In our main contribution, for each county techniques of small area estimation are used to borrow strength across counties and a pooled test of independence of BMD and BMI is obtained using a hierarchical Bayesian model. Our pooled Bayes test is computed by performing a Monte Carlo integration using random samples rather than Gibbs samples. We have seen important differences among the pooled Bayes test, direct Bayes test and the Cressie-Read test that allows for some degree of sparseness, when the degree of evidence against independence is studied. As expected, we also found that the direct Bayes test is sensitive to the prior specifications but the pooled Bayes test is not so sensitive. Moreover, the pooled Bayes test has competitive power properties, and it is superior when the cell counts are small to moderate.     

New innovational outlier unit root test with a break at an unknown time

The Perron test which is based on a Dickey–Fuller test regression is a commonly employed approach to test for a unit root in the presence of a structural break of unknown timing. In the case of an innovational outlier (IO), the Perron test tends to exhibit spurious rejections in finite samples when the break occurs under the null hypothesis. In the present paper, a new Perron-type IO unit root test is developed. It is shown in Monte Carlo experiments that the new test does not over-reject the null hypothesis. Even for the case of a level and slope break for trending data, the empirical size is near its nominal level. The test distribution equals the case of a known break date. Furthermore, the test is able to identify the true break date very accurately even for small breaks. As an application serves the Nelson–Plosser data set.     

A permutation test for the spread of three-dimensional rotation data

The permutation test is a nonparametric test that can be used to compare measures of spread for two data sets, but is yet to be explored in the context of three-dimensional rotation data. A permutation test for such data is developed and the statistical power of this test is considered under various conditions. The test is then used in a brief application comparing movement around the calcaneocuboid joint for a human, chimpanzee, and baboon.     

A Correlation Test for Normality Based on the Lévy Characterization

A powerful test of fit for normal distributions is proposed. Based on the Lévy characterization, the test statistic is the sample correlation coefficient of normal quantiles and sums of pairs of observations from a random sample. Since the test statistic is location-scale invariant, critical values can be obtained by simulation without estimating any parameters. It is proved that this test is consistent. A power comparison study including some directed tests shows that the proposed test is competitive, it is more powerful than the well-known Jarque–Bera test, and it is comparable to Shapiro–Wilk test against a number of alternatives.     

Testing the equality of the variances of two linear models

Testing the equality of variances of two linear models with common β-parameter is considered. A test based on least squares residuals (ASR test) is proposed, and it is shown that this test is invariant under the group of scale and translation changes. For some special cases, it is also proved that this test has a monotone power function. Finding the exact critical values of this test is not easy; an approximation is given to facilitate the computation of these. The powers of the BLUS test, the F-test and the new test are computed for various alternatives and compared in a particular case. The proposed test seems to be locally more powerful than the alternative tests.     

Accurate tests for the equality of coefficients of variation

ABSTRACT

A frequently encountered statistical problem is to determine if the variability among k populations is heterogeneous. If the populations are measured using different scales, comparing variances may not be appropriate. In this case, comparing coefficient of variation (CV) can be used because CV is unitless. In this paper, a non-parametric test is introduced to test whether the CVs from k populations are different. With the assumption that the populations are independent normally distributed, the Miller test, Feltz and Miller test, saddlepoint-based test, log likelihood ratio test and the proposed simulated Bartlett-corrected log likelihood ratio test are derived. Simulation results show the extreme accuracy of the simulated Bartlett-corrected log likelihood ratio test if the model is correctly specified. If the model is mis-specified and the sample size is small, the proposed test still gives good results. However, with a mis-specified model and large sample size, the non-parametric test is recommended.     

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.     

AN EXACT TEST FOR HAZARD SIMILARITY

An exact test is developed for hazard similarity and in particular for exponentiality. This test is distinct from more common goodness-of-fit tests such as the Kolmogorov–Smirnov goodness-of-fit test, as it does not require full specification of the null distribution. This test is obtained through a characterization of hazard-similar distributions and a generalization of Fisher's test for association.     

A Nonparametric Test for Granger Causality in Distribution With Application to Financial Contagion

This article introduces a kernel-based nonparametric inferential procedure to test for Granger causality in distribution. This test is a multivariate extension of the kernel-based Granger causality test in tail event. The main advantage of this test is its ability to examine a large number of lags, with higher-order lags discounted. In addition, our test is highly flexible because it can be used to identify Granger causality in specific regions on the distribution supports, such as the center or tails. We prove that the test converges asymptotically to a standard Gaussian distribution under the null hypothesis and thus is free of parameter estimation uncertainty. Monte Carlo simulations illustrate the excellent small sample size and power properties of the test. This new test is applied to a set of European stock markets to analyze spillovers during the recent European crisis and to distinguish contagion from interdependence effects.