Strong uniform convergence of the recursive regression estimator under φ-mixing conditions

Suppose the observations (X_i, Y_i) taking values in R^d×R, are -mixing. Compared with the i.i.d. case, some known strong uniform convergence results for the estimators of the regression function r(x)=E(Y_i|X_i=x) need strong moment conditions under -mixing setting. We consider the following improved kernel estimators of r(x) suggested by Cheng (1983): Qian and Mammitzsch (2000) investigated the strong uniform convergence and convergence rate for to r(x) under weaker moment conditions than those of the others in the literature, and the optimal convergence rate can be attained under almost the same conditions as stated in Theorem 3.3.2 of Györfi et al. (1989). In this paper, under the similar conditions of Qian and Mammitzsch (2000), we study the strong uniform convergence and convergence rates for (j=2,3) to r(x), which have not been discussed by Qian and Mammitzsch (2000). In contrast to , our estimators and are recursive, which is highly desirable for practical computation.     

Rough-and-ready assessment of the degree and importance of smoothing in functional estimation

In nonparametric estimation of functionals of a distribution, it may or may not be desirable, or indeed necessary, to introduce a degree of smoothing into this estimation. In this article, I describe a method for assessing, with just a little thought about the functional of interest, (i) whether smoothing is likely to prove worthwhile, and (ii) if so, roughly how much smoothing is appropriate (in order-of-magnitude terms). This rule-of-thumb is not guaranteed to be accurate nor does it give a complete answer to the smoothing problem. However, I have found it very useful over a number of years; many examples of its use, and limitations, are given.     

Relative efficiency and deficiency of kernel type estimators of smooth distribution functions

Abstract  The problem is investigated whether a given kernel type estimator of a distribution function at a single point has asymptotically better performance than the empirical estimator. A representation of the relative deficiency of the empirical distribution function with respect to a kernel type estimator is established which gives a complete solution to this problem. The problem of finding optimal kernels is studied in detail.     

向量分整序列非线性变换的研究

自Granger提出整数阶单整向量序列的协整概念以来,协整理论在国内外学者的共同努力下不断得到完善。关于向量时间序列的分数维单整的研究主要集中在分整的线性协整的存在性条件及性质研究。文中通过引入交换条件数学期望算法(ACE),研究分整时间序列的非线性变换的协整性,对最优非线性变换函数进行估计。     

Some model-restricted shrinkage estimators for contingency tables with missing data

For contingency tables with extensive missing data, the unrestricted MLE under the saturated model, computed by the EM algorithm, is generally unsatisfactory. In this case, it may be better to fit a simpler model by imposing some restrictions on the parameter space. Perlman and Wu (1999) propose lattice conditional independence (LCI) models for contingency tables with arbitrary missing data patterns. When this LCI model fits well, the restricted MLE under the LCI model is more accurate than the unrestricted MLE under the saturated model, but not in general. Here we propose certain empirical Bayes (EB) estimators that adaptively combine the best features of the restricted and unrestricted MLEs. These EB estimators appear to be especially useful when the observed data is sparse, even in cases where the suitability of the LCI model is uncertain. We also study a restricted EM algorithm (called the ER algorithm) with similar desirable features. Received: July 1999     

Strong uniform convergence for the estimator of the regression function under ϕ-mixing conditions

Suppose the observations (X _i,Y _i), i=1,…, n, are ϕ-mixing. The strong uniform convergence and convergence rate for the estimator of the regression function was studied by serveral authors, e.g. G. Collomb (1984), L. Gy?rfi et al. (1989). But the optimal convergence rates are not reached unless the Y _i are bounded or the E exp (a|Y _i|) are bounded for some a>0. Compared with the i.i.d. case the convergence of the Nadaraya-Watson estimator under ϕ-mixing variables needs strong moment conditions. In this paper we study the strong uniform convergence and convergence rate for the improved kernel estimator of the regression function which has been suggested by Cheng P. (1983). Compared with Theorem A in Y. P. Mack and B. Silverman (1982) or Theorem 3.3.1 in L. Gy?rfi et al. (1989), we prove the convergence for this kind of estimators under weaker moment conditions. The optimal convergence rate for the improved kernel estimator is attained under almost the same conditions of Theorem 3.3.2 in L. Gy?rfi et al. (1989). Received: September 1999     

Modelling Regional Welfare Efficiency Applying Conditional Full Frontiers

Abstract

This paper demonstrates an evaluation of welfare policies and regional allocation of public investment using the recent developments in efficiency analysis and statistical inference. Specifically, the efficiency of the welfare policies of the Greek prefectures for the census years of 1980, 1990 and 2000 are compared and analyzed. The paper, using bootstrap techniques on unconditional and conditional full frontier applications, indicates that there are major welfare inefficiencies among the prefectures over the three census years. The analysis reveals that the increase of population density over the years has a negative impact on the welfare efficiency levels of the Greek prefectures.

RÉSUMÉ Cette communication démontre une évaluation des politiques sociales et de l'affectation régionale d'investissements publics, sur la base de développements récents dans l'analyse du rendement et des conclusions statistiques. Plus spécifiquement, nous comparaisons et nous analysons l'efficacité des politiques sociales des préfectures grecques pour les années de recensement 1980, 1990 et 2000. En appliquant des techniques de rééchantillonnage à des applications à frontières intégrales inconditionnelles et conditionnelles, la communication démontre que les années de recensement ont été marquées par l'existence d'une grande inefficacité sur le plan social, parmi les préfectures. L'analyse révèle que l'augmentation de la densité de la population a, au fil des années, eu un effet négatif sur l'efficacité des préfectures de la Grèce sur le plan social.

R esumen Este estudio demuestra una evaluación de las políticas de beneficios sociales y la distribución regional de la inversión pública usando los recientes desarrollos en análisis de eficiencia e inferencia estadística. Específicamente, se compara y analiza la eficiencia de las políticas de beneficios sociales de las prefecturas griegas en los años de censo 1980, 1990 y 2000. El estudio que usa técnicas bootstrap en las aplicaciones de frontera completa incondicionales y condicionales indica que existen importantes ineficiencias en los beneficios sociales entre las prefecturas durante los tres años censados. El análisis revela que el aumento de la densidad de la población a través de los años tiene un impacto negativo en los niveles de eficiencia de los beneficios sociales en las prefecturas griegas.

     

Stability of characterizations of normal distributions based on the conditional expected values of the sample skewness and the sample kurtosis

Characterizations of normal distributions given by Nguyen and Dinh (1998) based on conditional expected values of the sample skewness and the sample kurtosis, given the sample mean and the sample variance, are shown to be stable. Received: September 1998