A good property of the maximum likelihood estimator in a restricted normal model

Summary We consider a normal model with known diagonal covariance matrix and a vector of means constrained to belong to a polyhedral cone. The standard estimatorsX (unrestricted MLE) andX ^* (restricted MLE) are compared for estimation of several components of the parameter simultaneously. We show thatX ^* is preferred toX under several conditions.     

Robust consideration of importance sampling in digital communication system

Abstract

This paper proposes using a mixed biasing distribution in Importance Sampling for estimating the bit error rate (BER) via Monte Carlo simulation. The proposed mixed biasing distribution is more robust than the commonly used Gaussian tail distribution when the signal or the threshold setting is disturbed by a uniformly distributed random noise. In this paper the robustness is quantified by the mean squared error.     

An MSE comparison of the restricted Stein-rule and minimum mean squared error estimators in regression

In this paper, we consider the feasible minimum mean squared error (FMMSE) estimator and the adjusted FMMSE (AFMMSE) estimator which are obtained by shrinking the ordinary least squares (OLS) estimator towards the restricted least squares estimator. We derive the formulas of MSE for the restricted FMMSE and AFMMSE estimators. By numerical evaluations, the MSE performances of the restricted FMMSE and AFMMSE estimators are compared with that of the restricted positive-part Stein-rule estimator.     

The Use of LaGrange Multipliers with Response Surfaces

Using LaGrange multipliers an example is given wherein the optimum level of a fitted second order response function is obtained subject to a constraint provided by another fitted second order response function.     

Choosing the smoothing parameter for unordered multinomial data

We consider the estimation of multinomial probabilities in the non-sparse univariate unordered case. We describe a number of explicit methods (mostly pre-existing) for the choice of the smoothing parameter in this context. In simulations, we compare these methods in terms of mean root mean squared error performance. Our recommendation is for the routine use of the simplest Bayesian estimation formula in which the probability in thek'th cell is estimated by (n _k +1)/(N+K) wheren _k is the count in thek'th cell,N is the sample size andK is the number of cells.     

Phase I control chart based on a kernel estimator of the quantile function

To measure the statistical performance of a control chart in Phase I applications, the in‐control average run length (ARL) is the most frequently used parameter. In typical start up situations, control limits must be computed without knowledge of the underlying distribution of the quality characteristic. Assumptions of an underlying normal distribution can increase the probability of false alarms when the underlying distribution is non‐normal, which can lead to unnecessary process adjustments. In this paper, a control chart based on a kernel estimator of the quantile function is proposed. Monte Carlo simulation was used to evaluate the in‐control ARL performance of this chart relative to that of the Shewhart individuals control chart. The results indicate that the proposed chart is more robust to deviations in the assumed underlying distribution (with respect to the in‐control ARL) and results in an alternative method of designing control charts for individual units. Copyright © 2011 John Wiley & Sons, Ltd.     

More Comments on Cp

I study the typical configuration of a C_p plot when the number of variables in the regression problem is large and there are many weak effects. I show that a particular configuration that is very commonly seen can arise in a simple way. I give a formula by means of which the risk incurred by the “minimum C_P ” rule can be estimated.     

基于邻域阈值分类的小波域图像去噪算法

利用图像小波系数的空间相关性可以有效地去除图像中的噪声。将一维信号的小波邻域阈值扩展并应用于二维图像,子带内的每个小波系数根据其邻域阈值的大小被划分为“大”系数或者是“小”系数;对“小”系数直接置零,对“大”系数则采用一种具有局部空间强相关性的零均值高斯模型,通过最小均方误差准则得到其估计。仿真实验结果表明该算法简单有效,在去噪性能上优于传统的子带自适应阈值去噪方法,可与两种优秀的空间自适应去噪算法相媲美。     

The multivariate extremal index and the dependence structure of a multivariate extreme value distribution

LetH be the limiting distribution of a vector of maxima for ad-dimensional stationary sequnce with multivariate extremal index. We giv necessary and sufficient conditions forH to have independent or totally dependent margins by using relations between the multivariate extremal index and the univariate extremal indexes. A new functional family of multivariates extreme value distributions, containingH, is introduced. We apply the results to characterize the asymptotic independence of the maximum and the minimum and compute the multivariate extremal index of the Multivariate Maxima of Moving Maxima process.     

基于均方差快速增强的图像修复算法

在分析几种关键图像修复算法的实现原理、适用性及其优劣的基础上,针对目前图像修复算法可能存在适用性有限、优化修复算法中存在的算法复杂度较高或者未考虑破损图像的结构信息的情况,提出了一种基于数据融合的加权均方差快速增强图像修复算法,并将其应用于壁画和自然图像的修复实验中。通过系统仿真实验证明,在修复强结构纹理自然图像和壁画时该方法能紧密结合图像结构信息进行有效地修复,同时,其适用性在原有的基础上有所提高。     

Discussion

The use of Stein estimation in multiple linear regression is considered. Tables and graphs are presented that compare the prediction mean squared errors of positive-part James-Stein, preliminary-test, reduced, and full-model least squares estimates. The appropriateness of using Stein contraction on possibly extraneous variables is emphasized, and a procedure is presented for evaluating the likely savings in using Stein estimation on the problem at hand. An example is given.     

Bayesian analysis for weighted mean‐squared error in dual response surface optimization

Dual response surface optimization considers the mean and the variation simultaneously. The minimization of mean‐squared error (MSE) is an effective approach in dual response surface optimization. Weighted MSE (WMSE) is formed by imposing the relative weights, (λ, 1?λ), on the squared bias and variance components of MSE. To date, a few methods have been proposed for determining λ. The resulting λ from these methods is either a single value or an interval. This paper aims at developing a systematic method to choose a λ value when an interval of λ is given. Specifically, this paper proposes a Bayesian approach to construct a probability distribution of λ. Once the distribution of λ is constructed, the expected value of λ can be used to form WMSE. Copyright © 2009 John Wiley & Sons, Ltd.     

The extreme value theory approach to safety estimation

Crash-based safety analysis is hampered by several shortcomings, such as randomness and rarity of crash occurrences, lack of timeliness, and inconsistency in crash reporting. Safety analysis based on observable traffic characteristics more frequent than crashes is one promising alternative. In this research, we proposed a novel application of the extreme value theory to estimate safety. The method is considered proactive in that it no longer requires historical crash data for the model calibration. We evaluated the proposed method by applying it to right-angle collisions at signalized intersections. Evaluation results indicated a promising relationship between safety estimates and historical crash data. Crash estimates at seven out of twelve sites remained within the range of Poisson-based confidence intervals established using historical crash data. The test has yielded large-variance safety estimates due to the short 8-h observation period. A simulation experiment conducted in this study revealed that 3-6 weeks of observation are needed to obtain safety estimates with confidence intervals comparable to those being obtained from 4-year observed crash counts. The proposed method can be applied to other types of locations and collisions as well.     

Diffusion Based Channel Gains Estimation in WSN Using Fractional Order Strategies

In this study, it is proposed that the diffusion least mean square (LMS) algorithm can be improved by applying the fractional order signal processing methodologies. Application of Caputo’s fractional derivatives are considered in the optimization of cost function. It is suggested to derive a fractional order variant of the diffusion LMS algorithm. The applicability is tested for the estimation of channel parameters in a distributed environment consisting of randomly distributed sensors communicating through wireless medium. The topology of the network is selected such that a smaller number of nodes are informed. In the network, a random sleep strategy is followed to conserve the transmission power at the nodes. The proposed fractional order modified diffusion LMS algorithms are applied in the two configurations of combine-then-adapt and adapt-then-combine. The average squared error performance of the proposed algorithms along with its traditional counterparts are evaluated for the estimation of the Rayleigh channel parameters. A mathematical proof of convergence is provided showing that the addition of the nonlinear term resulting from fractional derivatives helps adjusts the autocorrelation matrix in such a way that the spread of its eigenvalues decreases. This increases the convergence as well as the steady state response even for the larger step sizes. Experimental results are shown for different number of nodes and fractional orders. The simulation results establish that the accuracy of the proposed scheme is far better than its classical counterparts, therefore, helps better solves the channel gains estimation problem in a distributed wireless environment. The algorithm has the potential to be applied in other applications related to learning and adaptation.     

Confidence Interval Estimation for the Weibull and Extreme Value Distributions

This paper reviews methods of constructing confidence intervals for parameters or other characteristics of the Weibull or extreme value distribution. The conditional method of obtaining confidence intervals is stressed, with emphasis on the flexibility of the method, and on the computations which are necessary to use it.     

A constitutive relation error estimator based on traction‐free recovery of the equilibrated stress

A new methodology for recovering equilibrated stress fields is presented, which is based on traction‐free subdomains' computations. It allows a rather simple implementation in a standard finite element code compared with the standard technique for recovering equilibrated tractions. These equilibrated stresses are used to compute a constitutive relation error estimator for a finite element model in 2D linear elasticity. A lower bound and an upper bound for the discretization error are derived from the error in the constitutive relation. These bounds in the discretization error are used to build lower and upper bounds for local quantities of interest. Copyright © 2008 John Wiley & Sons, Ltd.     

On error estimator and p‐adaptivity in the generalized finite element method

This paper addresses the issue of a p‐adaptive version of the generalized finite element method (GFEM). The technique adopted here is the equilibrated element residual method, but presented under the GFEM approach, i.e., by taking into account the typical nodal enrichment scheme of the method. Such scheme consists of multiplying the partition of unity functions by a set of enrichment functions. These functions, in the case of the element residual method are monomials, and can be used to build the polynomial space, one degree higher than the one of the solution, in which the error functions is approximated. Global and local measures are defined and used as error estimator and indicators, respectively. The error indicators, calculated on the element patches that surrounds each node, are used to control a refinement procedure. Numerical examples in plane elasticity are presented, outlining in particular the effectivity index of the error estimator proposed. Finally, the ‐adaptive procedure is described and its good performance is illustrated by the last numerical example. Copyright © 2004 John Wiley & Sons, Ltd.     

Testing the hypothesis of a general linear model using nonparametric regression estimation

Summary Given the modelY _i =m(χ _i )+ɛi,whereE(ɛ _i) =0,X _i ≠Ci=1, ...,n, andC is ap-dimensional compact set, we have designed a new method for testing the hypothesis that the regression function follows a general linear model,m(·) ∈ {m _θ(·) =A ^t (·)θ}_{θ∈Θ⊂ℛq} , withA a function fromℜ ^p toℜ ^q. The statistic, denoted ΔASE, used fortesting the given hypothesis is defined to be the difference between the average squared errors (ASE) associated with the non-parametric estimator ofm and the minimum distance parametric estimator ofm. The asymptotic normality of both ΔASE and the minimum distance estimators is proved under general conditions. Alternative bootstrap versions of ΔASE are also considered.     

分层先验总体中总体总量的经验贝叶斯预测

对具有分层逆伽马先验总体中总体总量的经验贝叶斯预测进行研究。首先,提出一种新方法得到总体总量的贝叶斯预测,并在此基础上获得总体总量的经验贝叶斯预测。其次,分情形探讨了经验贝叶斯预测的性质,结果表明它是渐近最优的,并在预测均方误差意义下优于最佳线性无偏预测。最后,通过模拟研究论证了论文的主要结论。     

Proceedings of the Computer Science and Statistics: 12th Annual Symposium on the Interface

This article examines the properties of smoothed estimators of the probabilities of misclassification in linear discriminant analysis and compares them with those of the resubstitution, leave-one-out, and bootstrap estimators. Smoothed estimators are found to have smaller variance than the other estimators and bias that is a function of the amount of smoothing. An algorithm is presented for determining a reasonable level of smoothing as a function of the training sample sizes and the number of dimensions in the observation vector. Using the criterion of unconditional mean squared error, this particular smoothed estimator, called the NS method, appears to offer a reasonable alternative to existing nonparametric estimators.