Jean-Claude Massé

A Monte Carlo study of the accuracy and robustness of ten bivariate location estimators

In a Monte Carlo study, ten bivariate location estimators are compared as regards their accuracy and robustness. In addition to the arithmetic mean, five bivariate medians and four depth-based trimmed means are thus investigated. The behavior of the estimators is examined under various sampling situations determined by three sample sizes and 26 underlying distributions, 14 of which are centrally symmetric and 12 are asymmetric contaminated normals. Performance is assessed through numerical functions of the sample mean squared error and bias matrices.

Multivariate reciprocal stationary Gaussian processes

In this paper we examine the characterization of multivariate reciprocal stationary Gaussian processes in terms of their covariance matrix function. As an illustration, we identify all second-order reciprocal Gaussian processes.

A counterexample on the existence of the L1-median

On the Banach space of real sequences converging to 0, it is shown that a probability measure may not possess an L1-median inside the space. This puts into better perspective previous results of existence of L1-medians obtained by Valadier and Kemperman.

Representations for multivariate reciprocal Gaussian processes

Multivariate reciprocal Gaussian processes are represented as a sum of two independent processes: a piecewise Markov process, which is also represented in terms of a Wiener-type process, and a time-dependent linear transformation of a normally distributed random vector. This result is then applied to the first-passage time problem. >

On multiple Markov chains

The aim of this paper is to examine multiple Markov dependence for the discrete as well as for the continuous parameter case. In both cases the Markov property with arbitrary parameter values is investigated and it is shown that it leads to the degeneration of the multiple Markov dependence to the simple one.

Reciprocal covariance solutions of some matrix differential equations

In this paper necessary and sufficient conditions are given for the solutions of certain homogeneous matrix differential equations with constant coefficients to be covariance matrix functions of a class of multivariate reciprocal stationary Gaussian processes. These conditions involve only the coefficients of the equations and the initial values. Several examples illustrate the results obtained.

Nonparametric maximum likelihood estimation in a non locally compact setting

Maximum likelihood estimation is considered in the context of infinite dimensional parameter spaces. It is shown that in some locally convex parameter spaces sequential compactness of the bounded sets ensures the existence of minimizers of objective functions and the consistency of maximum likelihood estimators in an appropriate topology. The theory is applied to revisit some classical problems of nonparametric maximum likelihood estimation, to study location parameters in Banach spaces, and finally to obtain Varadarajan’s theorem on the convergence of empirical measures in the form of a consistency result for a sequence of maximum likelihood estimators. Several parameter spaces sharing the crucial compactness property are identified.

A Monte Carlo Study of the Robustness of Prediction in Growth Curve Models

Prediction methods for growth curve models often assume that, for each case in the sample, the vector of measurements has a multivariate normal distribution with an appropriate covariance structure. In a two-part Monte Carlo study, we investigate the effect of nonnormality on the accuracy of several commonly used predictors. In the first part, the covariance structure is taken to be of the so-called uniform or serial forms; next the behavior of the same predictors is examined assuming that the data is contaminated according to a mixture of normals model, where most of the observations arise from a distribution with a uniform or serial structure, but the overall covariance structure is arbitrary. The predictors are seen to be robust in the first case, but potentially quite inaccurate in the second case.