V. Alba-Fernández

Goodness-of-fit tests based on empirical characteristic functions

A class of goodness-of-fit tests based on the empirical characteristic function is studied. They can be applied to continuous as well as to discrete or mixed data with any arbitrary fixed dimension. The tests are consistent against any fixed alternative for suitable choices of the weight function involved in the definition of the test statistic. The bootstrap can be employed to estimate consistently the null distribution of the test statistic. The goodness of the bootstrap approximation and the power of some tests in this class for finite sample sizes are investigated by simulation.

Minimum ϕ-divergence estimation in misspecified multinomial models

The consequences of model misspecification for multinomial data when using minimum [phi]-divergence or minimum disparity estimators to estimate the model parameters are considered. These estimators are shown to converge to a well-defined limit. Two applications of the results obtained are considered. First, it is proved that the bootstrap consistently estimates the null distribution of certain class of test statistics for model misspecification detection. Second, an application to the model selection test problem is studied. Both applications are illustrated with numerical examples.

Bias Correction in the Type I Generalized Logistic Distribution

Four strategies for bias correction of the maximum likelihood estimator of the parameters in the Type I generalized logistic distribution are studied. First, we consider an analytic bias-corrected estimator, which is obtained by deriving an analytic expression for the bias to order n −1; second, a method based on modifying the likelihood equations; third, we consider the jackknife bias-corrected estimator; and fourth, we consider two bootstrap bias-corrected estimators. All bias correction estimators are compared by simulation. Finally, an example with a real data set is also presented.

Bootstrapping divergence statistics for testing homogeneity in multinomial populations

We consider the problem of testing the equality of @n (@n>=2) multinomial populations, taking as test statistic a sample version of an f-dissimilarity between the populations, obtained by the replacement of the unknown parameters in the expression of the f-dissimilarity among the theoretical populations, by their maximum likelihood estimators. The null distribution of this test statistic is usually approximated by its limit, the asymptotic null distribution. Here we study another way to approximate it, the bootstrap. We show that the bootstrap yields a consistent distribution estimator. We also study by simulation the finite sample performance of the bootstrap distribution and compare it with the asymptotic approximation. From the simulations it can be concluded that it is worth calculating the bootstrap estimator, because it is more accurate than the approximation yielded by the asymptotic null distribution which, in addition, cannot always be exactly computed.

Divergence statistics for testing uniform association in cross-classifications

In this paper, we consider the problem of testing uniform association in cross-classifications having ordered categories, taking as test statistic one in the family proposed by Conde and Salicru [J. Conde, M. Salicru, Uniform association in contingency tables associated to Csiszar divergence, Statistics and Probability Letters 37 (1998) 149-154]. We consider two approximations to the null distribution of the test statistics in this family: an estimation of the asymptotic null distribution and a bootstrap estimator. We prove that both approximations are asymptotically equivalent. To study their finite sample performance, we carried out two simulation experiments, whose results are presented. From the simulations it can be concluded that the bootstrap estimator behaves much better than the estimated asymptotic null distribution.

Two classes of divergence statistics for testing uniform association

The problem of testing uniform association in cross-classifications having ordered categories is considered. Two families of test statistics, both based on divergences between certain functions of the observed data, are studied and compared. Our theoretical study is based on asymptotic properties. For each family, two consistent approximations to the null distribution of the test statistic are studied: the asymptotic null distribution and a bootstrap estimator; all the tests considered are consistent against fixed alternatives; finally, we do a local power study. Surprisingly, both families detect the same local alternatives. The finite sample performance of the tests in these two classes is numerically investigated through some simulation experiments. In the light of the obtained results, some practical recommendations are given.

A bootstrap algorithm for the two-sample problem using trigonometric Hermite spline interpolation

Abstract In this paper we study the two-sample problem using procedures based on the empirical characteristic function. We consider the L 2 norm of the difference between the empirical characteristic functions and use an interpolant to obtain a numerical integration formula to approximate the test statistic. For our approximation method we have used a trigonometric Hermite interpolant, and afterwards, to estimate the p -value of the resultant statistic, a bootstrap algorithm was implemented.

Testing for a class of bivariate exponential distributions

Bivariate and multivariate exponential distributions are widely applied in several areas such as reliability, queueing systems or hydrology. A frequently used bivariate exponential distribution is the Moran–Downton distribution. Because of this reason, this paper proposes a goodness-of-fit test for this distribution. The test statistic exploits the analytically convenient formula of its characteristic function. Large sample properties of the proposed test such as consistency against fixed and local alternatives are studied. The finite sample performance is numerically studied. Finally, an application of this distribution to hydrological data is presented.

Erratum to Divergence statistics for testing uniform association in cross-classifications [Inform. Sci. 180 (2010) 4557-4571]

The indices in the sum in Theorem 1 on page 4560 do not match. Next we give the correct version of this theorem. Let H be an orthonormal matrix (I 1)(J 1) (I 1)(J 1)-matrix such that 1 c2 DRD t 1⁄4 Hdiagðk1; k2; . . . ; km;0ÞH. Recall that the set {k1,k2, . . . ,km} are the non-null eigenvalues of 1 c2 DRD t as in (1) of the paper. Let d 1⁄4 c HDd 1⁄4 ðd t 1; d2Þ t , with d1 2 Rm and d2 2 R. Theorem 1. Under the contiguous alternative hypothesis H1,n,