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## Goodness-of-fit tests for semiparametric and parametric hypotheses based on the probability weighted empirical characteristic function

### Statistical Papers (2016-12-01) 57: 957-976 , December 01, 2016

We investigate the finite-sample properties of certain procedures which employ the novel notion of the probability weighted empirical characteristic function. The procedures considered are: (1) Testing for symmetry in regression, (2) Testing for multivariate normality with independent observations, and (3) Testing for multivariate normality of random effects in mixed models. Along with the new tests alternative methods based on the ordinary empirical characteristic function as well as other more well known procedures are implemented for the purpose of comparison.

## Selecting the Best Population Using a Test for Equality Based on Minimal Wilcoxon Rank-sum Precedence Statistic

### Methodology and Computing in Applied Probability (2007-06-01) 9: 263-305 , June 01, 2007

In this paper, we first give an overview of the precedence-type test procedures. Then we propose a nonparametric test based on early failures for the equality of two life-time distributions against two alternatives concerning the best population. This procedure utilizes the minimal Wilcoxon rank-sum precedence statistic (Ng and Balakrishnan, 2002, 2004) which can determine the difference between populations based on early (100*q*%) failures. Hence, this procedure can be useful in life-testing experiments in biological as well as industrial settings. After proposing the test procedure, we derive the exact null distribution of the test statistic in the two-sample case with equal or unequal sample sizes. We also present the exact probability of correct selection under the Lehmann alternative. Then, we generalize the test procedure to the *k*-sample situation. Critical values for some sample sizes are presented. Next, we examine the performance of this test procedure under a location-shift alternative through Monte Carlo simulations. Two examples are presented to illustrate our test procedure with selecting the best population as an objective.

## Testing for one-sided alternatives in nonparametric censored regression

### TEST (2012-09-01) 21: 498-518 , September 01, 2012

Assume that we have two populations (*X*_{1},*Y*_{1}) and (*X*_{2},*Y*_{2}) satisfying two general nonparametric regression models *Y*_{j}=*m*_{j}(*X*_{j})+*ε*_{j}, *j*=1,2, where *m*(⋅) is a smooth location function, *ε*_{j} has zero location and the response *Y*_{j} is possibly right-censored. In this paper, we propose to test the null hypothesis *H*_{0}:*m*_{1}=*m*_{2} versus the one-sided alternative *H*_{1}:*m*_{1}<*m*_{2}. We introduce two test statistics for which we obtain the asymptotic normality under the null and the alternative hypotheses. Although the tests are based on nonparametric techniques, they can detect any local alternative converging to the null hypothesis at the parametric rate *n*^{−1/2}. The practical performance of a bootstrap version of the tests is investigated in a simulation study. An application to a data set about unemployment duration times is also included.

## On the optimal choice of the number of empirical Fourier coefficients for comparison of regression curves

### Statistical Papers (2015-11-01) 56: 981-997 , November 01, 2015

The paper is devoted to the elaboration of an efficient approach for comparison of two regression curves based on the empirical Fourier coefficients of regression functions. For the problem of testing for the equality of the two unknown functions in the case of homoscedastic error structure and observation at equidistant points, we derive a new procedure with adaptive choice of the number of the coefficients used in the hypotheses testing. Our approach is based on approximation of the most powerful test using the full knowledge of the regression functions. The results are justified by theoretical arguments and the superiority of the new procedure is also confirmed by a simulation study.

## Recent and classical tests for exponentiality: a partial review with comparisons

### Metrika (2005-02-01) 61: 29-45 , February 01, 2005

### Abstract.

A wide selection of classical and recent tests for exponentiality are discussed and compared. The classical procedures include the statistics of Kolmogorov-Smirnov and Cramér-von Mises, a statistic based on spacings, and a method involving the score function. Among the most recent approaches emphasized are methods based on the empirical Laplace transform and the empirical characteristic function, a method based on entropy as well as tests of the Kolmogorov-Smirnov and Cramér-von Mises type that utilize a characterization of exponentiality via the mean residual life function. We also propose a new goodness-of-fit test utilizing a novel characterization of the exponential distribution through its characteristic function. The finite-sample performance of the tests is investigated in an extensive simulation study.

## Asymptotic efficiency of new exponentiality tests based on a characterization

### Metrika (2016-02-01) 79: 221-236 , February 01, 2016

Two new tests for exponentiality, of integral- and Kolmogorov-type, are proposed. They are based on a recent characterization and formed using appropriate V-statistics. Their asymptotic properties are examined and their local Bahadur efficiencies against some common alternatives are found. A class of locally optimal alternatives for each test is obtained. The powers of these tests, for some small sample sizes, are compared with different exponentiality tests.

## A permutation test for comparing rotational symmetry in three-dimensional rotation data sets

### Journal of Statistical Distributions and Applications (2017-09-29) 4: 1-8 , September 29, 2017

Although there have been fairly recent advances regarding inference for three-dimensional rotation data, there are still many areas of interest yet to be explored. One such area involves comparing the rotational symmetry of 3-D rotations. In this paper, nonparametric inference is used to test if *F*_{1}=*F*_{2}, where *F*_{i} is the degree of rotational symmetry of distribution *i*, through a permutation test. The validity of the developed permutation test is examined through a simulation study and the test is applied to a small example in biomechanics.

## Testing skew normality via the moment generating function

### Mathematical Methods of Statistics (2010-03-01) 19: 64-72 , March 01, 2010

In this paper, goodness-of-fit tests are constructed for the skew normal law. The proposed tests utilize the fact that the moment generating function of the skew normal variable satisfies a simple differential equation. The empirical counterpart of this equation, involving the empiricalmoment generating function, yields appropriate test statistics. The consistency of the tests is investigated under general assumptions, and the finite-sample behavior of the proposed method is investigated via a parametric bootstrap procedure.

## Detecting distributional changes in samples of independent block maxima using probability weighted moments

### Extremes (2017-06-01) 20: 417-450 , June 01, 2017

The analysis of seasonal or annual block maxima is of interest in fields such as hydrology, climatology or meteorology. In connection with the celebrated method of block maxima, we study several tests that can be used to assess whether the available series of maxima is identically distributed. It is assumed that block maxima are independent but not necessarily generalized extreme value distributed. The asymptotic null distributions of the test statistics are investigated and the practical computation of approximate p-values is addressed. Extensive Monte-Carlo simulations show the adequate finite-sample behavior of the studied tests for a large number of realistic data generating scenarios. Illustrations on several environmental datasets conclude the work.

## Approximations for weighted Kolmogorov–Smirnov distributions via boundary crossing probabilities

### Statistics and Computing (2017-11-01) 27: 1513-1523 , November 01, 2017

A statistical application to Gene Set Enrichment Analysis implies calculating the distribution of the maximum of a certain Gaussian process, which is a modification of the standard Brownian bridge. Using the transformation into a boundary crossing problem for the Brownian motion and a piecewise linear boundary, it is proved that the desired distribution can be approximated by an *n*-dimensional Gaussian integral. Fast approximations are defined and validated by Monte Carlo simulation. The performance of the method for the genomics application is discussed.