Consistency of jackknife estimators of the variances of simple quantiles

Let σ² be the asymptotic variance of the sample p-quantile (0<p<1). Consistency of the delete-d jackknife estimators of σ² with d being a fraction of n is proved under very weak conditions. Some other results, such as the asymptotic orders of the moments of the jackknife histograms and an analog of the generalized Helly's theorem, are also established.     

An implicit function based procedure for analyzing maximum likelihood estimates from nonidentically distributed data

A methodology is presented for gaining insight into properties — such as outlier influence, bias, and width of confidence intervals — of maximum likelihood estimates from nonidentically distributed Gaussian data. The methodology is based on an application of the implicit function theorem to derive an approximation to the maximum likelihood estimator. This approximation, unlike the maximum likelihood estimator, is expressed in closed form and thus it can be used in lieu of costly Monte Carlo simulation to study the properties of the maximum likelihood estimator.     

中值定理“中间点”渐近性研究的新进展(I)

综述了近年来在中值定理“中间点”渐近性方面取得的若干新成果 ,同时 ,提出了笔者认为值得进一步讨论的问题     

Extended Glivenko–Cantelli Theorem in Nonparametric Regression

In this paper, we consider the uniform strong consistency of the cumulative distribution function estimator in nonparametric regression. We obtain the extended Glivenko–Cantelli theorem for the residual-based empirical distribution function.     

Discusion

Resumen

En esta investigación se estudia la validez de una versión castellana de la escala «Environmental Concern Scale» (ECS) llevada a cabo con 716 estudiantes. Las puntuaciones obtenidas por los sujetos proambientalistas y no proambientalistas resultan significativamente diferentes. Asímismo, se estudian las relaciones entre las actitudes hacia la preocupación por el medio ambiente, la energía nuclear y la ideología política, mostrándose una relación entre ellas de diferente intensidad. Mientras la energía nuclear está fuertemente vinculada a la ideología política, no sucede en tal medida entre ésta y las actitudes conservacionistas, ya que tanto los de derechas como los de izquierdas participan de la preocupación por el medio ambiente, aunque no en la misma medida.     

Takacs–Fiksel Method for Stationary Marked Gibbs Point Processes

Abstract. This article studies a method to estimate the parameters governing the distribution of a stationary marked Gibbs point process. This procedure, known as the Takacs–Fiksel method, is based on the estimation of the left and right hand sides of the Georgii–Nguyen–Zessin formula and leads to a family of estimators due to the possible choices of test functions. We propose several examples illustrating the interest and flexibility of this procedure. We also provide sufficient conditions based on the model and the test functions to derive asymptotic properties (consistency and asymptotic normality) of the resulting estimator. The different assumptions are discussed for exponential family models and for a large class of test functions. A short simulation study is proposed to assess the correctness of the methodology and the asymptotic results.     

An integral representation technique for calculating general multivariate probabilities with an application to multivariate x2

Recently in Dutt (1973, (1975), intgral representations over (0,A) were obtained for upper and lover multivariate normal and the probilities. It was pointed out that these integral representaitons when evaluated by Gauss-Hermite uadrature yield rapid and accurate numerical results.

Here integral representaitons, based on an integral formula due to Gurland (1948), are indicated for arbitrary multivariate probabilities. Application of this general representaion for computing multivariate x2 probabilities is discussed and numerical results using Gaussian quadrature are given for the bivariate and equicorre lated trivariate cases. Applications to the multivariate densities studied by Miller (1965) are also included     

On Estimating the Integrated Co-Volatility Using Noisy High-Frequency Data with Jumps

In this article, we consider the estimation of covariation of two asset prices which contain jumps and microstructure noise, based on high-frequency data. We propose a realized covariance estimator, which combines pre-averaging method to remove the microstructure noise and the threshold method to reduce the jumps effect. The asymptotic properties, such as consistency and asymptotic normality, are investigated. The estimator allows very general structure of jumps, for example, infinity activity or even infinity variation. Simulation is also included to illustrate the performance of the proposed procedure.     

谈几类中值定理辅助函数的构造方法

给出三类中值定理辅助函数的构造方法.     

对共同基金定理的重新认识——不完整市场研究

本文就不完整市场提出了对连续时间共同基金定理的重新认识。这一新认识的提出同样摆脱了以往研究中对投资者消费和最终财富效用函数的假设。同样的，这些效用函数也都是可时间累加的、非减的函数。这项理论延伸也是基于离散过程和线性代数的简单属性。本文的研究结果适用于不完整市场。另外，以往只适用于包含单一风险资产的完整市场的最优投资策略自动延伸至包含多个风险资产的不完整市场。文中举出了一个实例。