On the behaviour of tests based on sample spacings for moderatesamples

We revisit the question about optimal performance of goodness-of-fit tests based on sample spacings. We reveal the importance of centering of the test-statistic and of the sample size when choosing a suitable test-statistic from a family of statistics based on power transformations of sample spacings. In particular, we find that a test-statistic based on empirical estimation of the Hellinger distance between hypothetical and data-supported distribution does possess some optimality properties for moderate sample sizes. These findings confirm earlier statements about the robust behaviour of the test-statistic based on the Hellinger distance and are in contrast to findings about the asymptotic (when sample size approaches infinity) of statistics such as Moran's and/or Greenwood's statistic. We include simulation results that support our findings.     

Asymptotic power of tests of normality under local alternatives

Seven tests of univariate normality are studied in view of their asymptotic power under local alternatives. The procedures under consideration are either based on the empirical skewness and/or kurtosis, including the popular Jarque-Bera statistic, as well as Cramér-von Mises, Anderson-Darling and Kolmogorov-Smirnov functionals of an empirical process with estimated parameters. The large-sample behavior of these test statistics under contiguous sequences is obtained; this allows for the computation of their associated local power curves and of their asymptotic relative efficiency in the light of a measure proposed by Berg and Quessy (2009). Comparisons are made under four classes of local alternatives, including those used by Thadewald and Büning (2007) in a recent Monte-Carlo power study. These theoretical results are related to empirical ones and many recommendations are formulated.     

Goodness-of-fit tests for parametric regression with selection biased data

Consider the nonparametric location-scale regression model Y=m(X)+σ(X)ε$Y=m(X)+\sigma (X)\epsilon$, where the error ε$\epsilon$ is independent of the covariate X$X$, and m$m$ and σ$\sigma$ are smooth but unknown functions. The pair (X,Y)$(X,Y)$ is allowed to be subject to selection bias. We construct tests for the hypothesis that m(·)$m(·)$ belongs to some parametric family of regression functions. The proposed tests compare the nonparametric maximum likelihood estimator (NPMLE) based on the residuals obtained under the assumed parametric model, with the NPMLE based on the residuals obtained without using the parametric model assumption. The asymptotic distribution of the test statistics is obtained. A bootstrap procedure is proposed to approximate the critical values of the tests. Finally, the finite sample performance of the proposed tests is studied in a simulation study, and the developed tests are applied on environmental data.     

Testing goodness-of-fit for some lifetime distributions with conventional Type-I censoring

A goodness-of-fit test procedure is proposed for some lifetime distributions when the available data are subject to Type-I censoring. The proposed method extends the test procedure of Pakyari and Balakrishnan to other lifetime distributions. The extension to Weibull and log-normal models is studied in details. The new test recovers the nominal level of significance and exhibits more power in comparison to the existing tests for several alternative distributions by means of Monte Carlo simulations. Finally, a real dataset is considered for illustrative purposes.     

On testing the skew normal hypothesis

In this work two goodness-of-fit tests are proposed for the skew normal distribution, based on properties of this family of distributions and the sample correlation coefficient. The critical values for the tests are obtained by using Monte Carlo simulation for several sample sizes and levels of significance. The power of the proposed tests are compared with that of the tests studied by Mateu et al. (2007) and the one studied by Meintanis (2007) for several sample sizes and considering diverse alternatives. The results show that the proposed tests have greater power than those studied by Mateu et al. (2007) and Meintanis (2007) against some alternative distributions.     

A Goodness-of-Fit Test for a Class of Autoregressive Conditional Duration Models

This article develops a method for testing the goodness-of-fit of a given parametric autoregressive conditional duration model against unspecified nonparametric alternatives. The test statistics are functions of the residuals corresponding to the quasi maximum likelihood estimate of the given parametric model, and are easy to compute. The limiting distributions of the test statistics are not free from nuisance parameters. Hence, critical values cannot be tabulated for general use. A bootstrap procedure is proposed to implement the tests, and its asymptotic validity is established. The finite sample performances of the proposed tests and several other competing ones in the literature, were compared using a simulation study. The tests proposed in this article performed well consistently throughout, and they were either the best or close to the best. None of the tests performed uniformly the best. The tests are illustrated using an empirical example.     

Simple and Exact Empirical Likelihood Ratio Tests for Normality Based on Moment Relations

The empirical likelihood (EL) technique is a powerful nonparametric method with wide theoretical and practical applications. In this article, we use the EL methodology in order to develop simple and efficient goodness-of-fit tests for normality based on the dependence between moments that characterizes normal distributions. The new empirical likelihood ratio (ELR) tests are exact and are shown to be very powerful decision rules based on small to moderate sample sizes. Asymptotic results related to the Type I error rates of the proposed tests are presented. We present a broad Monte Carlo comparison between different tests for normality, confirming the preference of the proposed method from a power perspective. A real data example is provided.     

Bootstrap misspecification tests for ARCH based on the empirical process of squared residuals

We propose and study by means of simulations and graphical tools a class of goodness-of-fit tests for ARCH models. The tests are based on the empirical distribution function of squared residuals and smooth (parametric) bootstrap. We examine empirical size and power by means of a simulation study. While the tests have overall correct size, their power strongly depends on the type of alternative and is particularly high when the assumption of Gaussian innovations is violated. As an example, the tests are applied to returns on Foreign Exchange rates.     

Multivariate portmanteau test for structural VARMA models with uncorrelated but non-independent error terms

We consider portmanteau tests for testing the adequacy of structural vector autoregressive moving-average (VARMA) models under the assumption that the errors are uncorrelated but not necessarily independent. The structural forms are mainly used in econometrics to introduce instantaneous relationships between economic variables. We first study the joint distribution of the quasi-maximum likelihood estimator (QMLE) and the noise empirical autocovariances. We then derive the asymptotic distribution of residual empirical autocovariances and autocorrelations under weak assumptions on the noise. We deduce the asymptotic distribution of the Ljung-Box (or Box-Pierce) portmanteau statistics in this framework. It is shown that the asymptotic distribution of the portmanteau tests is that of a weighted sum of independent chi-squared random variables, which can be quite different from the usual chi-squared approximation used under independent and identically distributed (iid) assumptions on the noise. Hence we propose a method to adjust the critical values of the portmanteau tests. Monte Carlo experiments illustrate the finite sample performance of the modified portmanteau test.     

Chi-Squared Goodness-of-Fit Tests for Parametric Accelerated Failure Time Models

We give chi-squared goodness-of fit tests for parametric regression models such as accelerated failure time, proportional hazards, generalized proportional hazards, frailty models, transformation models, and models with cross-effects of survival functions. Random right censored data are used. Choice of random grouping intervals as data functions is considered.