Stable limits for empirical processes on vapnik-cervonenk is classes of functions

Alexander' s (1987) central limit theorem for empirical processes on Vapnik-Cervonenkis classes of functions is extended to the case with non-Gaussian stable limits. The corresponding weak laws of large numbers are also established

The central limit theorem for empirical processess on V-C classes: a majorizing measure approach

Alexander (1987) gave necessary and sufficient conditions for the central limit theorem for empirical processes on Vapnik-Cervonenkis classes of functions. In this paper we present a different version of his result using Talagrand's analytic characterization of pregaussianness (the majorizing measure condition). Our proof can be directly extended to give the corresponding result in the non-gaussian stable case

A rate of convergence in clustering analysis

We present a result about stochastic boundedness of stable empirical processes on Vapnik-Cervonenkis classes of functions and we apply it to obtain a rate of convergence for the approximation between the sample and the populational variation in the k-centroids problem in clustering analysis

A rate of convergence in clustering analysis.

We present a result about stochastic boundedness of stable empirical processes on Vapnik-Cervonenkis classes of functions and we apply it to obtain a rate of convergence for the approximation between the sample and the populational variation in the k-centroids problem in clustering analysis.Clustering analysis; K-centroids; Empirical processes; Vapnik-Cervonenkis classes of functions;

Stable limits for empirical processes on vapnik-cervonenk is classes of functions.

Alexander' s (1987) central limit theorem for empirical processes on Vapnik-Cervonenkis classes of functions is extended to the case with non-Gaussian stable limits. The corresponding weak laws of large numbers are also established.Empirical processes; Vapnik-Cervonenkis classes of functions; Stable domains of attraction;

On the estimation of the influence curve

We prove the asymptotic validity of bootstrap confidence bands for the influence curve from its usual estimator (the sensitive curve). The proof is based on the use of Gill's (1989) generalized delta method for Hadamard differentiable operators. The scope and applicability of this result are also discussed

Bootstrapping unit root AR(1) models

We propose abootstrap resampling scheme for the least squares estimator of the parameter of an unstable first-order autoregressive model and we prove its asymptotic validity. This method is alternative to the invalid one studied by Basawa et al. (1991)

Bootstrap tests for unit root AR(1) models

In this paper, we propose bootstrap tests for unit roots in first-order autoregressive models. We provide the bootstrap functional limit theory needed to prove the asymptotic validity of these tests both for independent and autoregressive errors; in this case, the usual corrections due to innovations dependence can be avoided. We also present a power empirical study comparing these tests with existing alternative methods

Random coefficient regressions: parametric goodness of fit tests

Random coefficient regression models have been applied in different fields during recent years and they are a unifying frame for many statistical models. Recently, Beran and Hall (1992) opened the question of the nonparametric study of the distribution of the coefficients. Nonparametric goodness of fit tests were considered in Delicado and Romo (1994.). In this paper we propose statistics for parametric goodness of fit tests and we obtain their asymptotic distributions. Moreover, we construct bootstrap approximations to these distributions, proving their validity. Finally, a simulation study illustrates our results

Goodness of fit tests in random coefficient regression models

Random coefficient regressions have been applied in a wide range of fields, from biology to economics, and constitute a common frame for several important statistical models. A nonparametric approach to inference in random coefficient models was initiated by Beran and Hall. In this paper we introduce and study goodness of fit tests for the coefficient distributions; their asymptotic behaviour under the null hypothesis is obtained. We also propose bootstrap resampling strategies to approach these distributions and prove their asymptotic validity using results by Gine and Zinn on bootstrap empirical processes. A simulation study illustrates the properties of these tests