A Location Invariant Hill-Type Estimator

The Hill's estimator (Hill, 1975) has been largely used in extreme value theory in order to estimate the tail index associated to a distribution function with a positive index. One of the criticisms to its use is the possible associated bias, dependent on the top portion of the original sample used, and also the fact that it is not location invariant. Here, a new Hill-type estimator is studied, which is location invariant. This new estimator is based on the original Hill's estimator, but is made location invariant by a random shift. Its asymptotic distributional behavior is derived, in a semiparametric setup. A comparative simulation study is also presented for several models, following an appropriate adaptive procedure.     

A New Estimator for a Tail Index

We investigate properties of a new estimator for a tail index introduced by Davydov and co-workers. The main advantage of this estimator is the simplicity of the statistic used for the estimator. We provide results of simulation by comparing plots of our's and Hill's estimators.     

Large deviation theorem for Hill's estimator

To estimate the exponent of a regularly varying d.f. F, the asymptotic behaviour of Hill's estimator has been extensively discussed. Under the assumption that the d.f. F is continuous, we obtain the large deviation theorem for Hill's estimator. Project supported by the National Natural Science Foundation of China     

Alternatives to a Semi-Parametric Estimator of Parameters of Rare Events—The Jackknife Methodology*

In this paper, and in a context of regularly varying tails, we propose different alternatives to a well-known estimator of the tail index—the Hill estimator (Hill, 1975). These alternatives have essentially in mind a reduction in bias, preferably without increasing Mean Square Error, by the use of suitable Generalized Jackknife methodologies (Gray and Schucany, 1972). The first estimate obtained through this methodolgy is the one introduced by Peng (1998), under a different context. Other Generalized Jackknife estimators are linear combinations of Hill estimators at different levels. This methodology of affine combinations of Hill estimators at different levels may be easily generalized to other semi-parametric estimators of the tail index, like Pickands' estimator (Pickands, 1975) or the Moment's estimator (Dekkers et al., 1989), and consequently to a general real tail index, seeming to be a promising field of research.     

A POSTERIORI ERROR ESTIMATES FOR A MODIFIED WEAK GALERKIN FINITE ELEMENT APPROXIMATION OF SECOND ORDER ELLIPTIC PROBLEMS WITH DG NORM

In this paper,we derive a residual based a posteriori error estimator for a modified weak Galerkin formulation of second order elliptic problems.We prove that the error estimator used for interior penalty discontinuous Galerkin methods still gives both upper and lower bounds for the modified weak Galerkin method,though they have essentially different bilinear forms.More precisely,we prove its reliability and efficiency for the actual error measured in the standard DG norm.We further provide an improved a priori error estimate under minimal regularity assumptions on the exact solution.Numerical results are presented to verify the theoretical analysis.     

Variational Solutions for Eigenvalues of Single and Coupled Lam? Equations

The approach of Taylor & Arscott for the evaluation of eigenvaluesfor singly periodic Lam? equations is modified by truncatingthe infinite matrix representing Hill's equation to finite size.For two separate Lam? equations with a common separation constantA and a linear relation between their eigenvalues, A is foundby Newton's method; the required derivatives are expressed asexpectation values. Truncation to five or six rows is adequatefor most practical purposes. The results of Taylor for the deltawing problem are verified for small A, but for larger valuesof A perturbation expansions are shown to lead to quantitativelyand qualitatively erroneous results.     

非线性连续统力学应变率和应力率的近期探讨

本文对连续统力学的两个基本概念——应变率和应力率——进行了若干考虑,并提出一些结果.首先对应变和应力概念作了一个扼要的系统回顾.第二节用绝对符号法给出一个至今尚属未知的右伸长张量时间变化率的显表达式.尔后,本工作提议区分定义客观性应力率的两种途径.按照第二种途径分析了若干特例之后,作者提出一个称为广义Jaumann导数的作为客观性应力率.它包含了大部分现有的应力率定义,以及Hill的结果.     

Nonparametric estimators of the survival function with twice censored data

Patilea and Rolin (Ann Stat 34(2):925–938, 2006) proposed a product-limit estimator of the survival function for twice censored data. In this article, based on a modified self-consistent (MSC) approach, we propose an alternative estimator, the MSC estimator. The asymptotic properties of the MSC estimator are derived. A simulation study is conducted to compare the performance between the two estimators. Simulation results indicate that the MSC estimator outperforms the product-limit estimator and its advantage over the product-limit estimator can be very significant when right censoring is heavy.     

Prediction of the bearing capacity of composite flanges for aircraft-engine casing parts

Computed results of the stress-strain state of four different composite flanges for aircraft engines are presented for assigned external-load parameters, and their most heavily loaded regions are defined. The static strength of the structures is found from the stresses in the layers using the maximum-stress criterion and Hill's modified criterion. It is established that transverse tensile stresses are most critical. The service life of the flanges is estimated on the basis of the fatigue-failure criterion of the weakest link.Perm' State Technical University. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 3, pp. 360–369, May–June, 1997.     

回归系数的广义根方估计及其模拟

文献[1,2]中提出了回归系数的根方估计~(k),当回归自变量间存在复共线关系时,~(k)较回归系数的最小二乘估计有所改善,本文将根方估计作一拓广,得出了回归系数的广义根方估计~(K),其中K为对角阵,文中证明了广义根方估计~(K)较~(k)能更有效地改善最小二乘估计,并给出了广义根方估计的显式解,在此基础上,提出了广义根方估计的显式解和一种确定k_i的方法。     

Methods for improvement in estimation of a normal mean matrix

This paper is concerned with the problem of estimating a matrix of means in multivariate normal distributions with an unknown covariance matrix under invariant quadratic loss. It is first shown that the modified Efron-Morris estimator is characterized as a certain empirical Bayes estimator. This estimator modifies the crude Efron-Morris estimator by adding a scalar shrinkage term. It is next shown that the idea of this modification provides a general method for improvement of estimators, which results in the further improvement on several minimax estimators. As a new method for improvement, an adaptive combination of the modified Stein and the James-Stein estimators is also proposed and is shown to be minimax. Through Monte Carlo studies of the risk behaviors, it is numerically shown that the proposed, combined estimator inherits the nice risk properties of both individual estimators and thus it has a very favorable risk behavior in a small sample case. Finally, the application to a two-way layout MANOVA model with interactions is discussed.     

Bootstrap estimation of the asymptotic variances of statistical functionals

A modified bootstrap estimator of the asymptotic variance of a statistical functional is studied. The modified bootstrap variance estimator circumvents the problem of the original bootstrap when the population distribution has heavy tails, and requires less stringent conditions for its consistency than the ordinary bootstrap variance estimator. The consistency of the modified bootstrap variance estimator is established for differentiable statistical functionals.     

广义最小二乘估计为BLUE的若干条件

本文给出了一般广义最小二乘估计为BLUE的一个充要条件及几个充分条件。     

A POSTERIORI ERROR ESTIMATE OF OPTIMAL CONTROL PROBLEM OF PDE WITH INTEGRAL CONSTRAINT FOR STATE

In this paper, we study adaptive finite element discretization schemes for an optimal control problem governed by elliptic PDE with an integral constraint for the state. We derive the equivalent a posteriori error estimator for the finite element approximation, which particularly suits adaptive multi-meshes to capture different singularities of the control and the state. Numerical examples are presented to demonstrate the efficiency of a posteriori error estimator and to confirm the theoretical results.     

一类纵向数据半参数模型估计的收敛速度

本文研究了一类纵向数据半参数模型参数和回归函数的估计问题.利用最小二乘法和一般的非参数权函数方法,获得了参数估计量的强收敛速度和回归函数估计量的一致收敛速度,推广了文献[4]的相应结果.     

方差分量的改进估计

本文研究一类方差分量模型中方差分量的改进估计问题,对单向分类随机模型的对应于随机效应的方差分量,我们研究了一个不变估计类,它包含了一些常用重要估计。证明了在均方误差准则下,在该估计类中不存在一致最优不变估计,且方差分析估计是不容许估计。在一个重要子估计类中,找到了一致最优估计。对于较一般的含两个方差分量的混合模型,我们研究了一个非负估计类的性质,给出了它们的分布,并建立了它们优于方差分析估计的充分     

Modified restricted Liu estimator in logistic regression model

?iray et al. (Commun Stat Simul Comput, 2014) proposed a restricted Liu estimator in logistic regression model with linear restrictions. However, this estimator did not satisfy the linear restrictions. In this paper, we introduce a modified restricted Liu estimator in logistic regression model with linear restrictions. Our results show that the new estimator satisfies the linear restrictions. We also discuss the properties of the new estimator under the matrix mean squared error criterion. Finally, a Monte Carlo study and a numerical example are given to show the performances of the new estimator.     

END样本最近邻密度估计的强相合速度

本文研究了扩展负相依(END)样本最近邻密度估计的强相合性问题.利用END序列的Bernstein型不等式和截尾的方法,获得了END样本最近邻密度估计的强相合速度,推广了NA样本和ND样本最近邻密度估计的相应结果.     

无重复因析试验中散度效应的ML估计

在无重复因析试验中,若因子A,B的散度效应显著,则不论其交互效应AB的散度效应是否显著,其散度效应的现有估计常常是有偏的,从而导致其被错误地识别为显著效应.提出了散度效应的一种新的估计方法(称为ML估计),并给出了ML估计的方差的精确表达形式,证明了在一类模型中,交互效应AB的散度效应的ML估计是无偏的.最后,将ML估计与现有的常用估计进行了比较.     

Consistent Lyapunov exponent Estimation for one-dimensional dynamical systems

Summary  The author proves the consistency of a nearest neighbor estimator of the Lyapunov exponent for a general class of one-dimensional ergodic dynamical systems. The author shows that this estimator has good practical properties on a set of simulations.