Agustín García Nogales

A note on kernel density estimation at a parametric rate

In the context of kernel density estimation, we give a characterization of the kernels for which the parametric mean integrated squared error (MISE) rate n −1 may be obtained, where n is the sample size. Also, for the cases where this rate is attainable, we give an asymptotic bandwidth choice that makes the kernel estimator consistent in mean integrated squared error at that rate and a numerical example showing the superior performance of the superkernel estimator when the bandwidth is properly chosen. †Research supported by Spanish Ministerio de Ciencia y Tecnología project MTM2005-06348.

Early morphologic changes following microwave endocardial ablation for treatment of chronic atrial fibrillation during mitral valve surgery.

Introduction: The aim of this study was to investigate the early qualitative and quantitative structural changes in the left atrial wall after endocardial microwave ablation in patients with chronic atrial fibrillation (AF) undergoing mitral surgery.

On conditional independence and the relationship between sufficiency and invariance under the Bayesian point of view

The concept of conditional independence is considered in the study of the relationship between sufficiency and invariance under a Bayesian point of view showing, among other results, that the conditional independence of the almost-invariant [sigma]-field and a sufficient [sigma]-field given its intersection is equivalent to its sampling conditional independence. In the Bayesian framework, an improvement upon a well-known and classical result of Stein is obtained.

Unbiased Estimation for the General Half-Normal Distribution

This work proposes unbiased estimators for the parameters of the general half-normal distribution that exhibit a better performance than the estimators based on maximum likelihood proposed in the literature. From these estimators, large sample confidence sets are also derived.

A weak notion of equivalence in Bayesian statistical theory

This paper introduces a weak notion of equivalence of [sigma]-fields in a Bayesian framework. Some results and examples are given to show the usefulness of this concept in the study of the relationship between the independence of two [sigma]-fields and the conditional independence given its intersection.

On the Use of Bayes Factor in Frequentist Testing of a Precise Hypothesis

This article deals with Bayes factors as useful Bayesian tools in frequentist testing of a precise hypothesis. A result and several examples are included to justify the definition of Bayes factor for point null hypotheses, without merging the initial distribution with a degenerate distribution on the null hypothesis. Of special interest is the problem of testing a proportion (joint with a natural criterion to compare different tests), the possible presence of nuisance parameters, or the influence of Bayesian sufficiency on this problem. The problem of testing a precise hypothesis under a Bayesian perspective is also considered and two alternative methods to deal with are given.

Strong invariance under a Bayesian point of view

Sufficiency on the parameter space is used to extend to the Bayesian case a strong notion of invariance, obtaining the sufficiency of the almost-invariant [sigma]-field . We also give some results about the completeness of , giving in passing two partial answers to a question of J.K. Ghosh.

Partial sufficiency and density estimation

In this paper, we study the usefulness of the concept of partial sufficiency, in the sense of Fraser, when it is applied to the problem of nonparametric density estimation.

Exhaustivity, completeness and almost invariance

In this paper, the relationship between exhaustivity (or sufficiency in the sense of Blackwell) and invariance is studied. An analogous result of two classical theorems of Hall, Wijsman and Ghosh (1965) and Berk (1972) on the relationship between sufficiency and invariance is given making use of a concept introduced here under the name of boundedG-completeness; in particular, we get the same conclusion under the assumptions of stability and bounded completeness.

Equivalencia de problemas de decisión

En este trabajo se introduce una definicion de equivalencia de problemas de decision. Los resultados y ejemplos que presentamos muestran que esta definicion de equivalencia se adapta bien a la metodologia de la estadisticaSummaryA general and strong notion of equivalence of decision problems is given. Some results and examples are given to show that this natural notion is well adapted to the methodology of statistics.ResumenEn este trabajo se introduce una definición de equivalencia de problemas de decisión. Los resultados y ejemplos que presentamos muestran que esta definición de equivalencia se adapta bien a la metodología de la estadística.