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.     

An Improved Hollander's Distribution-Free Test for Parallelism

Hollander (1970 Hollander , M. ( 1970 ). A distribution-free test for parallelism . J. Amer. Statist. Assoc. 65 : 387 – 394 .[Taylor & Francis Online] , [Google Scholar]) proposed a distribution-free signed rank test for testing parallelism of two regression lines. Hollander's test requires that the number of pairs of data in the two datasets must be equal and even. This requirement of the test is met by discarding observation pairs randomly from one or both datasets as needed. In this article, we propose that instead of discarding the observation pairs randomly, we add observation pairs randomly in one or both datasets as needed to meet the requirement of Hollander's test. By using simulation technique we show that the new test is a significant improvement over the original test of Hollander since the new test is consistently more powerful than the original test and provides narrower confidence intervals for the difference of the two slopes of the regression lines.     

A Flexible Nonparametric Test for Ordered and Umbrella Alternatives

A flexible and robust test for the ordered and umbrella alternatives is proposed in this paper. A two-step procedure is presented to make the proposed test be easily applicable. Type I error and power of the given approach are thoroughly investigated by extensive Monte Carlo studies.     

A Distribution Free Test for the Equality of Scales

Situations where scale parameters are not nuisance factors to be controlled but outcomes to be explained arise in many contexts such as quality control, agricultural production systems, experimental education, the pharmaceutical industry and biology. Tests for homogeneity of variances are often of interest also as a preliminary to analysis of variance, dose-response modelling or discriminant analysis. The literature on tests for the equality of scales is vast. A test which usually stands out in terms of power and robustness against non normality is the modified Levene W50 test, however in the literature no test is found to be the most powerful one for every distribution. The goal of the article is to propose an effective method for comparing scales. More precisely, we propose a test for the equality of scales that, even though was not the most powerful one for every distribution, it has good overall performance under every type of distribution. This test has the form of a combined resampling test. It is important to note that non combined tests show good performance only in particular contexts. Size and power of the proposed test are studied via simulation and compared with many other robust tests for scale. A practical application to industrial quality control is discussed.     

An extension of the Anderson–Darling k-sample test to arbitrary sample space partition sizes

In this paper we first show that the k-sample Anderson–Darling test is basically an average of Pearson statistics in 2?×?k contingency tables that are induced by observation-based partitions of the sample space. As an extension, we construct a family of rank test statistics, indexed by c?∈??, which is based on similarly constructed c?×?k partitions. An extensive simulation study, in which we compare the new test with others, suggests that generally very high powers are obtained with the new tests. Finally we propose a decomposition of the test statistic in interpretable components.     

Comparison of unweighted and weighted rank based tests for an ordered alternative in randomized complete block designs

In randomized complete block designs, a monotonic relationship among treatment groups may already be established from prior information, e.g., a study with different dose levels of a drug. The test statistic developed by Page and another from Jonckheere and Terpstra are two unweighted rank based tests used to detect ordered alternatives when the assumptions in the traditional two-way analysis of variance are not satisfied. We consider a new weighted rank based test by utilizing a weight for each subject based on the sample variance in computing the new test statistic. The new weighted rank based test is compared with the two commonly used unweighted tests with regard to power under various conditions. The weighted test is generally more powerful than the two unweighted tests when the number of treatment groups is small to moderate.     

A Confidence Interval and Test for the Mean of an Asymmetric Distribution

ABSTRACT

A confidence interval and test are obtained for the mean of an asymmetric distribution using a random sample of size n. The method is based on N. J. Johnson's (1978 Johnson , N. J. ( 1978 ). Modified, t tests and confidence intervals for asymmetrical populations. J. Amer. Statist. Assoc. 73 ( 363 ): 536 – 544 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) modified t-test, where terms of Cornish–Fisher expansions involving the third moment are used to adjust the conventional statistic to have more closely a Student's t-distribution with n ? 1 degrees of freedom. Johnson's (1978 Johnson , N. J. ( 1978 ). Modified, t tests and confidence intervals for asymmetrical populations. J. Amer. Statist. Assoc. 73 ( 363 ): 536 – 544 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) test cannot be inverted uniquely, so a corresponding confidence interval for the mean may be disjointed. However, an artificial term of small order can be added to make inversion of the test a uniquely defined operation, which prevents such disjointedness. The resulting one-sided and two-sided intervals perform better than others in the literature with skewed distributions, and have good performance with a normal distribution. The two-sided interval may be recommended for general use if the sample size is 10 or more and the nominal confidence coefficient is 95% or less, or if the sample size is 30 or more and the confidence coefficient is 99% or less.     

Generalizations of Mathisen's median test for comparing several treatments with a control

A distribution-free test for comparing several treatments with a control is proposed for one-way classified data. It is advantageous to use the test in life-testing experiments where testing time is expensive. The proposed test has a shorter expected duration than a previously proposed test by Slivka(1970). The optimal allocation of the experimental units to the treatments for two situations are given. In a simulation study the power of the test is compared with the power of Slivka's test. An extension of the test for two-way classified data is given     

An exact distribution-free test comparing two multivariate distributions based on adjacency

Summary.  A new test is proposed comparing two multivariate distributions by using distances between observations. Unlike earlier tests using interpoint distances, the new test statistic has a known exact distribution and is exactly distribution free. The interpoint distances are used to construct an optimal non-bipartite matching, i.e. a matching of the observations into disjoint pairs to minimize the total distance within pairs. The cross-match statistic is the number of pairs containing one observation from the first distribution and one from the second. Distributions that are very different will exhibit few cross-matches. When comparing two discrete distributions with finite support, the test is consistent against all alternatives. The test is applied to a study of brain activation measured by functional magnetic resonance imaging during two linguistic tasks, comparing brains that are impaired by arteriovenous abnormalities with normal controls. A second exact distribution-free test is also discussed: it ranks the pairs and sums the ranks of the cross-matched pairs.     

傅里叶型平滑结构突变下Dickey-Fuller检验的功效——兼论Shibor的平稳性

通过推导Dickey-Fuller检验功效函数,研究表明:即使中小型的傅里叶型结构突变,都会严重影响Dickey-Fuller检验的功效,从而使得含傅里叶型平滑结构突变的平稳过程被误判为单位根过程。使用3、6、9个月期和一年期Shibor日度数据发现:传统的ADF、PP、DF-GLS和KPSS几乎都指出Shibor是单位根过程;考虑平滑结构突变的单位根检验则在1%的显著性水平下拒绝了单位根的原假设,这表明Shibor是含结构突变的平稳过程。因此,预测Shibor和理解其动态行为必须考虑其结构突变特征。     

Test of Normality Against Generalized Exponential Power Alternatives

The family of symmetric generalized exponential power (GEP) densities offers a wide range of tail behaviors, which may be exponential, polynomial, and/or logarithmic. In this article, a test of normality based on Rao's score statistic and this family of GEP alternatives is proposed. This test is tailored to detect departures from normality in the tails of the distribution. The main interest of this approach is that it provides a test with a large family of symmetric alternatives having non-normal tails. In addition, the test's statistic consists of a combination of three quantities that can be interpreted as new measures of tail thickness. In a Monte-Carlo simulation study, the proposed test is shown to perform well in terms of power when compared to its competitors.     

Non parametric multiple comparisons of non nested rival models

The practice for testing homogeneity of several rival models is of interest. In this article, we consider a non parametric multiple test for non nested distributions in the context of the model selection. Based on the linear sign rank test, and the known union–intersection principle, we let the magnitude of the data to give a better performance to the test statistic. We consider the sample and the non nested rival models as blocks and treatments, respectively, and introduce the extended Friedman test version to compare with the results of the test based on the linear sign rank test. A real dataset based on the waiting time to earthquake is considered to illustrate the results.     

Moments of the quartic assignment statistic with an application to multiple regression

We present the first three exact moments of the symmetric quartic assignment statistic. Efficient computational formulas have been derived to overcome severe difficulties in third moment calculations. Two examples illustrate applications of the quartic assignment statistic: evaluation of significant “clustering” or “mixing”; and distribution-free tests for equality of several planar regression models. This article extends previous results on the cubic assignment statistic in Iyer and Vecchia (1989).     

Distribution- free test for slope in linear regression model with replications

Some distribution-free methods are suggested in the paper for testing the hypothesis about the slope parameter in a one-sample linear regression model with multiple observations at each level of independent variable. Asymptotic relative efficiencies of these tests are discussed, and the tests are compared with their nonparametric competitors.     

残差块形自助法在非对称单位根检验中的适用性

非对称单位根检验已成为时间序列分析中重要研究领域之一。而当随机干扰项之间具有一般性的自相关时,非对称单位根检验式中,由于不同的滞后阶会对统计量检验势产生至关重要的影响,因此采用残差块形自助法（RBB）对非对称单位根EG检验进行有效的改进研究,并对RBB法的适用性进行了模拟。结果表明：RBB法不仅在一定程度上降低了检验水平扭曲,而且大大提高了EG法的检验势。     

检验式设定错误对时间序列单位根检验小样本性质的影响

首先对单位根检验的两类常见的数据生成系统进行比较,然后利用蒙特卡洛实验研究了时间序列单位根检验式的设定问题。研究发现在利用DF检验和DF-GLS检验进行时间序列的单位根检验时,检验式设定错误直接影响着检验结果,尤其在推断时间序列是趋势平稳过程还是有时间趋势项的随机游走过程或有二阶时间趋势多项式的随机游走过程时,检验式的错误设定很容易将趋势平稳过程误判为非平稳过程。     

Distribution-free tests for independence against positive quadrant dependence: A generalization

A class of distribution-free tests based on two matched pairs is considered for testing independence against positive quadrant dependence. The class of tests proposed by Kochar and Gupta (1990) is a member of the proposed class. The performance of the proposed class is evaluated in terms of Pitman asymptotic relative efficiency for Block-Basu (1974) model and Woodworth family of distributions. The small sample performance of few members of the proposed class is also studied by finding empirical powers. Unbiasedness and consistency of the proposed class of tests have been established.     

What Do Interpolated Nonparametric Confidence Intervals for Population Quantiles Guarantee?

The interval between two prespecified order statistics of a sample provides a distribution-free confidence interval for a population quantile. However, due to discreteness, only a small set of exact coverage probabilities is available. Interpolated confidence intervals are designed to expand the set of available coverage probabilities. However, we show here that the infimum of the coverage probability for an interpolated confidence interval is either the coverage probability for the inner interval or the coverage probability obtained by removing the more likely of the two extreme subintervals from the outer interval. Thus, without additional assumptions, interpolated intervals do not expand the set of available guaranteed coverage probabilities.     

A general model for testing the proportional hazards and the accelerated failure time hypotheses in the analysis of censored survival data with covariates

Censored survival data are analysed by regression models which require some assumptions on the waycovariates affect the hazard function. Praportional Hazards (PH) and Accelerated Failure Times (AFT) are the hypothese most often used in practice. A method is introduced here for testing the PH and the AFT hypotheses against a general model for the hazard function. Simulated and real data arepresented to show the usefulness of the method.     

Estimating the variance of the sample median

The small-sample bias and root mean squared error of several distribution-free estimators of the variance of the sample median are examined. A new estimator is proposed that is easy to compute and tends to have the smallest bias and root mean squared error.