An exact Kolmogorov–Smirnov test for the Poisson distribution with unknown mean

We develop an exact Kolmogorov–Smirnov goodness-of-fit test for the Poisson distribution with an unknown mean. This test is conditional, with the test statistic being the maximum absolute difference between the empirical distribution function and its conditional expectation given the sample total. Exact critical values are obtained using a new algorithm. We explore properties of the test, and we illustrate it with three examples. The new test seems to be the first exact Poisson goodness-of-fit test for which critical values are available without simulation or exhaustive enumeration.     

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.     

Detection of non-Gaussianity

We develop two tests sensitive to various departures from composite goodness-of-fit hypothesis of normality. The tests are based on the sums of squares of some components naturally arising in decomposition of the Shapiro–Wilk-type statistic. Each component itself has diagnostic properties. The numbers of squared components in sums are determined via some novel selection rules based on the data. The new solutions prove to be effective tools in detecting a broad spectrum of sources of non-Gaussianity. We also discuss two variants of the new tests adjusted to verification of simple goodness-of-fit hypothesis of normality. These variants also compare well to popular competitors.     

Testing for noninferiority of binomial distributions referring to a modified equivalence region with piecewise linear boundary

In testing for noninferiority of two binomial distributions, the hypothesis formulation most commonly considered defines equivalence in terms of a constant bound to the difference of the two parameters. In order to avoid some basic logical difficulty entailed in this formulation we use an equivalence region whose boundary has fixed vertical distance from the diagonal for all values of the reference responder rate above some cutoff point and coincides left from this point with the line joining it with the origin. For the corresponding noninferiority hypothesis we derive and compare two different testing procedures. The first one is based on an objective Bayesian decision rule. The other one is obtained through combining the score tests for noninferiority with respect to the difference and the ratio of the two proportions, respectively, by means of the intersection–union principle. Both procedures are extensively studied by means of exact computational methods.     

Robust inference for Birnbaum–Saunders regressions

We propose a robust likelihood approach for the Birnbaum–Saunders regression model under model misspecification, which provides full likelihood inferences about regression parameters without knowing the true random mechanisms underlying the data. Monte Carlo simulation experiments and analysis of real data sets are carried out to illustrate the efficacy of the proposed robust methodology.     

Non-parametric testing for the number of change points in a sequence of independent random variables

A non-parametric procedure is derived for testing for the number of change points in a sequence of independent continuously distributed variables when there is no prior information available. The procedure is based on the Kruskal–Wallis test, which is maximized as a function of all possible places of the change points. The procedure consists of a sequence of non-parametric tests of nested hypotheses corresponding to a decreasing number of change points. The properties of this procedure are analyzed by Monte Carlo methods and compared to a parametric procedure for the case that the variables are exponentially distributed. The critical values are given for sample sizes up to 200.     

Wild-bootstrapped variance-ratio test for autocorrelation in the presence of heteroskedasticity

The Breusch–Godfrey LM test is one of the most popular tests for autocorrelation. However, it has been shown that the LM test may be erroneous when there exist heteroskedastic errors in a regression model. Recently, remedies have been proposed by Godfrey and Tremayne [9] and Shim et al. [21]. This paper suggests three wild-bootstrapped variance-ratio (WB-VR) tests for autocorrelation in the presence of heteroskedasticity. We show through a Monte Carlo simulation that our WB-VR tests have better small sample properties and are robust to the structure of heteroskedasticity.     

Comparing the BLUEs Under Two Linear Models

In this article, we consider two linear models, ?₁ = {y, X β, V ₁} and ?₂ = {y, X β, V ₂}, which differ only in their covariance matrices. Our main focus lies on the difference of the best linear unbiased estimators, BLUEs, of X β under these models. The corresponding problems between the models {y, X β, I _n } and {y, X β, V}, i.e., between the OLSE (ordinary least squares estimator) and BLUE, are pretty well studied. Our purpose is to review the corresponding considerations between the BLUEs of X β under ?₁ and ?₂. This article is an expository one presenting also new results.     

Some multivariate goodness-of-fit tests based on data depth

Based on data depth, three types of nonparametric goodness-of-fit tests for multivariate distribution are proposed in this paper. They are Pearson’s chi-square test, tests based on EDF and tests based on spacings, respectively. The Anderson–Darling (AD) test and the Greenwood test for bivariate normal distribution and uniform distribution are simulated. The results of simulation show that these two tests have low type I error rates and become more efficient with the increase in sample size. The AD-type test performs more powerfully than the Greenwood type test.