Hausman-type tests for individual and time effects in the panel regression model with incomplete data

By comparing estimators of the variance of idiosyncratic error at different robust levels, two Hausman-type test statistics are respectively constructed for the existence of individual and time effects in the panel regression model with incomplete data. The resultant test statistics have several desired properties. Firstly, they are robust to the presence of one effect when the other is tested. Secondly, they are immune to the non-normal distribution of the disturbances since the distributional conditions are not needed in the construction of the statistics. Thirdly, they have more robust performances than the main competitors in the literature when the covariates are correlated with the effects. Additionally, they are very simple and have no heavy computational burden. Joint tests for both of the two effects are also discussed. Monte Carlo evidence shows that the proposed tests have desired finite sample properties, and a real data analysis gives further support.     

A class of tests for exponentiality against decreasing mean residual life alternatives

A class of tests is proposed for testing Exponentiality against the Decreasing Mean Residual Life (DMRL) class of non-exponential probability distributions. These tests are consistent and asymptotically unbiased against all continuous DMRL alternatives. They are U - statistics and hence asymptotically normally distributed. The asymptotic relative efficiency (ARE) with respect to other tests for DMRL are quite high. Small sample powers are also comparable with small sample powers of the competitors.     

Small sample power of multivariate nonparametric tests for monotone trend

Bhattacharyya and Kioiz (1966) propose two multivariate nonparametric tests for monotone trend, one involving coordinate-wise Mann statistics and the other, coordinate-wise Spearman statistics. Dietz and Killeen (1981) propose a different test statistic based on coordinate-wise Mann statistics. The Pitman asymptotic relative efficiency of all three tests with respect to a normal theory competitor equals the cube root of the efficiency of a multivariate signed rank test with respect to Hotelling's T2. In this article, the small sample power of the nonparametric tests, the normal theory test, and a Bonferroni approach involving coordinate-wise univariate Mann or Spearman tests is examined in a simulation study. The Mann statistic of Dietz and Killeen and the Spearman statistic of Bhattacharyya and Klotz are found to perform well under both null and alternative hypotheses     

Robust statistics for testing equality of means or variances

For testing the equality of means (location parameters) of two populations, Tiku (1980a) defined a statistic Tc (based on symmetrically censored samples) and showed that this statistic is robust to underlying populations and is also remarkably powerful. In this paper, we define a similar statistic T (based on samples s with observations censored only on one side) and show that this stat is tic is more powerful than T and nonparametric statistics, C for skew populations. We also provide a modification of this statistic for testing the equality of two population variances.     

The Asymptotic Power Of Jonckheere-Type Tests For Ordered Alternatives

For the c -sample location problem with ordered alternatives, the test proposed by Barlow et al . (1972 p. 184) is an appropriate one under the model of normality. For non-normal data, however, there are rank tests which have higher power than the test of Barlow et al ., e.g. the Jonckheere test or so-called Jonckheere-type tests recently introduced and studied by Büning & Kössler (1996). In this paper the asymptotic power of the Jonckheere-type tests is computed by using results of Hájek (1968) which may be considered as extensions of the theorem of Chernoff & Savage (1958). Power studies via Monte Carlo simulation show that the asymptotic power values provide a good approximation to the finite ones even for moderate sample sizes.     

Efficiency of nonparametric tests for scale shift at an unknown time point

Recently Hsieh considered three nonparametric tests for the scale-change problem and showed them to be asymptotically as efficient as their parametric competitors. Here the class of so called sum-type statistics is studied which contains the statistics of Hsieh. It is proved that max-type statistics can be constructed that are at least as efficient in the sense of Bahadur as the sum-type statistics.     

An adaptive two-sample location-scale test of lepage type for symmetric distributions

For the two-sample location and scale problem we propose an adaptive test which is based on so called Lepage type tests. The well known test of Lepage (1971) is a combination of the Wilcoxon test for location alternatives and the Ansari-Bradley test for scale alternatives and it behaves well for symmetric and medium-tailed distributions. For the cae of short-, medium- and long-tailed distributions we replace the Wilcoxon test and the .Ansari-Bradley test by suitable other two-sample tests for location and scale, respectively, in oder to get higher power than the classical Lepage test for such distribotions. These tests here are called Lepage type tests. in practice, however, we generally have no clear idea about the distribution having generated our data. Thus, an adaptive test should be applied which takes the the given data set inio consideration. The proposed adaptive test is based on the concept of Hogg (1974), i.e., first, to classify the unknown symmetric distribution function with respect to a measure for tailweight and second, to apply an appropriate Lepage type test for this classified type of distribution. We compare the adaptive test with the three Lepage type tests in the adaptive scheme and with the classical Lepage test as well as with other parametric and nonparametric tests. The power comparison is carried out via Monte Carlo simulation. It is shown that the adaptive test is the best one for the broad class of distributions considered.     

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 wide review on exponentiality tests and two competitive proposals with application on reliability

In this paper, two new statistics based on comparison of the theoretical and empirical distribution functions are proposed to test exponentiality. Critical values are determined by means of Monte Carlo simulations for various sample sizes and different significance levels. Through an extensive simulation study, 50 selected exponentiality tests are studied for a wide collection of alternative distributions. From the empirical power study, it is concluded that, firstly, one of our proposals is preferable for IFR (increasing failure rate) and UFR (unimodal failure rate) alternatives, whereas the other one is preferable for DFR (decreasing failure rate) and BFR (bathtub failure rate) alternatives and, secondly, the new tests can be considered serious and powerful competitors to other existing proposals, since they have the same (or higher) level of performance than the best tests in the statistical literature.     

One-and two-sample sign tests for ranked set sample selective designs

Statistical inference based on a ranked set sample depends very much on the location of the quantified observations. A selective design which determines the location of the quantified observations in a ranked set sample is introduced. The paper investigates the effects of selective designs on one and two sample sign test statistics. The Pitman efficiencies of one- and two sample sign tests are calculated for selective designs and compared with ranked set samples of the same size. If the design quantifies observations at the center points, then the proposed procedure is superior to a ranked set sample of the same size in the sense of Pitman efficiency. Some practical problems are addressed for the two-sample sign test.     

Efficiency of nonparametric tests for scale shift at an unknown time point

Recently Hsieh considered three nonparametric tests for the scalechange problem and showed them to be asymptotically as efficient as their parametric competitors. Here the class of so called sum-type statistics is studied which contains the statistics of Hsieh. It is proved that max-type statistics can be constructed that are at least as efficient in the sense of Bahadur as the sum-type statistics.     

Nonparametric repeated significance tests for some analysis of covariance models

For a general class of nonparametric analysis of covariance problems (with stochastic covariates), some repeated significance testing procedures are developed. These procedures rest on the construction of suitable rank order statistics based on the partial sequence of sample sizes and allow for a monitoring of experimentation with the objective of a possible early termination of experimentation. The basic theory is based on the weak convergence of certain stochastic processes relating to the rank order statistics. Various properties of the proposed tests are discussed.     

Multivariate multi-sample tests for location based on data depth

A notion of data depth is used to measure centrality or outlyingness of a data point in a given data cloud. In the context of data depth, the point (or points) having maximum depth is called as deepest point (or points). In the present work, we propose three multi-sample tests for testing equality of location parameters of multivariate populations by using the deepest point (or points). These tests can be considered as extensions of two-sample tests based on the deepest point (or points). The proposed tests are implemented through the idea of Fisher's permutation test. Performance of earlier tests is studied by simulation. Illustration with two real datasets is also provided.     

Analyzing the results of a cloud-seeding experiment in tasmania

We considered the analysis or a randomized cloud seeding experiment of lusmania, Where an distributed analysis had been specified before the experiment was carried one. We compare “classical” regression analyses, with and without transformations, with permutation tests based upon double-ratio and variance-ratio statistics. Regression residuals are used to compare the merits of various other alternative test-statistics including some based upon gamma distribution assumptions. We conclude that more attention needs to be paid to the relative weights which various rest statistics implicitly attach to low, medium and high rainfalls, and that, irrespective ot distributional assumptions and theory, significant testing should be done using permutation tests.     

The Effect of a Variable Data Point on Hypothesis Tests for Means

The effect of a single variable data point, x, on the usual test statistics for traditional hypothesis tests for means is analyzed. It is shown that an outlier may have a profound and unexpected effect on the test statistic. Although it might appear that an outlier would tend to lend support to the alternate hypothesis, it may in fact detract from the significance of the test. In one-population tests and analysis of variance (ANOVA), the value of x that maximizes the significance of the test statistic is given. This value does not have to be unusually large or small. In fact, it often falls within the range of the other sample points. In the general one-population case, the limiting value for the test statistic is shown to be +1. In the case involving more than one population, it is shown that the limiting value of the test statistic is a function only of the number of members in the samples and not their relative values. Special cases are identified in which the test statistic is shown to have unique characteristics depending on the characteristics of the data.     

Goodness of fit and homogeneity tests on the basis of N-distances

In this paper we propose an application of N-distance theory [Klebanov, L.B., 2005. N-distances and their applications. Karolinum, Prague] for testing simple hypotheses of goodness of fit and homogeneity. The asymptotic null distribution of test statistics is established and coincides with the distribution of infinite quadratic form of independent standard normal random variables. A construction of multivariate free-of-distribution homogeneity test is considered. The power of proposed criteria is compared with classical tests using Monte-Carlo simulations.     

Comparisons of some tests for validation of stochastic simulation models

Properties of proposed parametric and nonparametric tests for the problem of validating stochastic simulation models are discussed. Asymptotic efficiencies for various types of alternatives are developed for some of the tests. Numerical procedures along with simulation methods are used to evaluate the adequacy of normal approximations to the null distributions of the statistics and the small-sample power of the tests.     

A new test for two-sample location problem based on empirical distribution function

We propose a new test for testing the equality of location parameter of two populations based on empirical distribution function (ECDF). The test statistics is obtained as a power divergence between two ECDFs. The test is shown to be distribution free, and its null distribution is obtained. We conducted empirical power comparison of the proposed test with several other available tests in the literature. We found that the proposed test performs better than its competitors considered here under several population structures. We also used two real datasets to illustrate the procedure.     

A new nonparametric bivariate test for two sample location problem

A strictly nonparametric bivariate test for two sample location problem is proposed. The proposed test is easy to apply and does not require the stringent condition of affine-symmetry or elliptical symmetry which is required by some of the major tests available for the same problem. The power function of the proposed test is calculated. The asymptotic distribution of the proposed test statistic is found to be normal. The power of proposed test is compared with some of the well-known tests under various distributions using Monte Carlo simulation technique. The power study shows that the proposed test statistic performs better than most of the test statistics for almost all the distributions considered here. As soon as the underlying population structure deviates from normality, the ability of the proposed test statistic to detect the smallest shift in location increases as compared to its competitors. The application of the test is shown by using a data set.     

Tests for Comparing Mark-Specific Hazards and Cumulative Incidence Functions

It is of interest in some applications to determine whether there is a relationship between a hazard rate function (or a cumulative incidence function) and a mark variable which is only observed at uncensored failure times. We develop nonparametric tests for this problem when the mark variable is continuous. Tests are developed for the null hypothesis that the mark-specific hazard rate is independent of the mark versus ordered and two-sided alternatives expressed in terms of mark-specific hazard functions and mark-specific cumulative incidence functions. The test statistics are based on functionals of a bivariate test process equal to a weighted average of differences between a Nelson-Aalen-type estimator of the mark-specific cumulative hazard function and a nonparametric estimator of this function under the null hypothesis. The weight function in the test process can be chosen so that the test statistics are asymptotically distribution-free. Asymptotically correct critical values are obtained through a simple simulation procedure. The testing procedures are shown to perform well in numerical studies, and are illustrated with an AIDS clinical trial example. Specifically, the tests are used to assess if the instantaneous or absolute risk of treatment failure depends on the amount of accumulation of drug resistance mutations in a subject's HIV virus. This assessment helps guide development of anti-HIV therapies that surmount the problem of drug resistance.