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We propose three new classes of goodness-of-fit tests for the Pareto type I distribution based on a characterization. The asymptotic null distribution for the tests are derived and their Bahadur efficiencies are compared to the efficiencies of some of the existing tests. It is found that the new integral type test has superior local efficiencies amongst the new tests, and in general, has higher efficiencies than the competing tests considered. The finite-sample performance of the newly proposed tests is evaluated and compared to that of other existing tests by means of a Monte Carlo study. It is found that the new tests (especially the integral type tests) perform favourably compared to the other tests.

We derive the efficiencies of two new tests for exponentiality which are based on a recent characterization that uses the idea of a random shift. The finite-sample performance of the newly proposed tests is evaluated and compared to other existing tests by means of Monte Carlo simulations. It is found that the new tests perform favourably when compared to the other tests. Overall the best performing tests seem to be our new Kolmogorov-Smirnov type test, the score function based test by Cox and Oakes, and the Kolmogorov-Smirnov type test based on the mean residual life. The tests are also applied to a real-world data set with i.i.d. data as well as to simulated data from a Cox-proportional hazards model, where we test whether the so-called Cox–Snell residuals follow a standard exponential distribution

The exponential distribution plays a key role in the practical application of reliability theory, survival analysis, engineering and queuing theory. These applications often rely on the underlying assumption that the observed data originate from an exponential distribution. In this paper, two new tests for exponentiality are proposed, which are based on a conditional second moment characterisation. The proposed tests are compared to various established tests for exponentiality by means of a simulation study where it is found that the new tests perform favourably relative to the existing tests. The tests are also applied to real-world data sets with independent and identically distributed data as well as to simulated data from a Cox proportional hazards model, to determine whether the residuals obtained from the fitted model follow a standard exponential distribution.

Quasi-stationary distributions have many applications in diverse research fields. We develop a bootstrap-based maximum likelihood (BML) method to deal with quasi-stationary distributions in statist...

We propose two new tests for symmetry based on well-known characterisations of symmetric distributions. The performance of the new tests is evaluated and compared to that of other existing tests by means of a Monte Carlo study. All tests are carried out in a regression setup where we test whether the error distribution in a linear regression model is symmetric. It is found that the newly proposed tests perform favourably compared to the other tests.

International audience; We propose and study new goodness-of-fit tests for the Rayleigh distribution based on a characterization involving a conditional expectation. The asymptotic properties of the tests are explored and the performance of the new tests are evaluated and compared to that of existing tests by means of a Monte Carlo study. It is found that the newly proposed tests perform satisfactory compared to the competitor tests.

International audience; We consider tests for serial independence of arbitrary finite order for the innovations in vector autoregressive models. The tests are expressed as L2-type criteria involving the difference of the joint empirical characteristic function and the product of corresponding marginals. Asymptotic as well as Monte-Carlo results are presented.

We propose a data-dependent method for choosing the tuning parameter appearing in many recently developed goodness-of-fit test statistics. The new method, based on the bootstrap, is applicable to a class of distributions for which the null distribution of the test statistic is independent of unknown parameters. No data-dependent choice for this parameter exists in the literature; typically, a fixed value for the parameter is chosen which can perform well for some alternatives, but poorly for others. The performance of the new method is investigated by means of a Monte Carlo study, employing three tests for exponentiality. It is found that the Monte Carlo power of these tests, using the data-dependent choice, compares favourably to the maximum achievable power for the tests calculated over a grid of values of the tuning parameter.

We introduce the notion of the probability weighted characteristic function (PWCF) as a generalization of the characteristic function. Some of the properties of the PWCF and of its empirical counterpart are studied and the potential use of these quantities in goodness-of-fit testing is examined in detail. The corresponding limiting null distributions and consistency results for location-scale models are derived and finite-sample comparisons are presented. Also, the notion of the PWCF is extended to arbitrary dimension Research Grant 11699 of the Special Account for Research Grants of the National and Kapodistrian University of Athens. National Research Foundation of South Africa

We derive the joint distribution of the ranks associated with a given bivariate random sample. Using these results, exact non-asymptotic expressions and asymptotic expansions for the mean and variance of the classical empirical copula estimator are obtained. An explicit expression of the coefficient appearing in the O ( 1 / n ) -term for the mean can, for example, be found; a result that apparently does not appear in the existing literature. Furthermore, it is shown that similar explicit non-asymptotic expressions as well as asymptotic expansions can be derived for the rank-based Bernstein copula estimator.

The traditional non-parametric bootstrap (referred to as the n-out-of-n bootstrap) is a widely applicable and powerful tool for statistical inference, but in important situations it can fail. It is well known that by using a bootstrap sample of size m, different from n, the resulting m-out-of-n bootstrap provides a method for rectifying the traditional bootstrap inconsistency. Moreover, recent studies have shown that interesting cases exist where it is better to use the m-out-of-n bootstrap in spite of the fact that the n-out-of-n bootstrap works. In this paper, we discuss another case by considering its application to hypothesis testing. Two new data-based choices of m are proposed in this set-up. The results of simulation studies are presented to provide empirical comparisons between the performance of the traditional bootstrap and the m-out-of-n bootstrap, based on the two data-dependent choices of m, as well as on an existing method in the literature for choosing m. These results show that the m-out-o...

This note analyses the problem of stability of hybrid simulation of dynamic systems. Time delays and sample-and-hold operations do cause serious stability problems, and if frequently happens that considerable time and effort are wasted because instability is not known in advance of programming the simulation on the hybrid computer. However, if the system under investigation can be approximated in its response by an equivalent linear system, then it is possible to define a procedure which will predict in advance whether any proposed computing scheme is stable. The text describes one such procedure, together with its implementation as a software package which can be used to predict the stability of simulations of practical size. In addition, the text contains a number of examples which illustrate the application of the software package.