Measurement error in proportional hazards models for survival data with long-term survivors

This work studies a proportional hazards model for survival data with "long-term survivors",in which covariates are subject to linear measurement error.It is well known that the naive estimators from both partial and full likelihood methods are inconsistent under this measurement error model.For measurement error models,methods of unbiased estimating function and corrected likelihood have been proposed in the literature.In this paper,we apply the corrected partial and full likelihood approaches to estimate the model and obtain statistical inference from survival data with long-term survivors.The asymptotic properties of the estimators are established.Simulation results illustrate that the proposed approaches provide useful tools for the models considered.     

当前状态数据下单变点危险率治愈模型的拟极大似然估计

变点危险率模型已受到广泛关注.它不仅可以更加直接地显示治疗效果或医学上的突破,也可以提供这些事件发生的时间点.在这篇文章中,我们提出当前状态数据下的单边点危险率治愈模型并探讨了这个模型的估计方法.我们建立了估计的大样本理论并通过模拟评估有限样本下的估计.     

Second derivative estimation using harmonic analysis

Simulation sensitivity analysis is an important problem for simulation practitioners analyzing complex systems. The significance of this problem has resulted in the development of various gradient estimators that can be used to address this issue. Although higher derivative estimators have been discussed concurrently, less attention has been given to assess the efficiency and feasibility of computing such estimators. In this paper, two second derivative estimators are presented. The first estimators, called the HFD estimators, combine harmonic gradient estimators with finite differences second derivative estimators. The resulting hybrid estimators requireO(p) fewer simulation runs to implement compared to the straightforward finite differences approach, wherep is the number of input parameters in the simulation model. The second estimators, called the HA estimators, incorporate harmonic analysis directly, requiring one or two simulation runs to implement, depending on whether a control variate simulation run is made. Expressions for the bias and the variance of the HFD and the HA estimators (with and without variance reduction techniques) are derived. Optimal mean squared error convergence rates are also discussed. In particular, the convergence rates for both these estimators are shown to be the same, though the computational performance of the HFD estimators is better than that for the HA estimators on anM/M/1 queue simulation model. Computational results for the HFD estimators on an (s, S) inventory system simulation model are also included.     

Safe and tight linear estimators for global optimization

Global optimization problems are often approached by branch and bound algorithms which use linear relaxations of the nonlinear constraints computed from the current variable bounds. This paper studies how to derive safe linear relaxations to account for numerical errors arising when computing the linear coefficients. It first proposes two classes of safe linear estimators for univariate functions. Class-1 estimators generalize previously suggested estimators from quadratic to arbitrary functions, while class-2 estimators are novel. When they apply, class-2 estimators are shown to be tighter theoretically (in a certain sense) and almost always tighter numerically. The paper then generalizes these results to multivariate functions. It shows how to derive estimators for multivariate functions by combining univariate estimators derived for each variable independently. Moreover, the combination of tight class-1 safe univariate estimators is shown to be a tight class-1 safe multivariate estimator. Finally, multivariate class-2 estimators are shown to be theoretically tighter (in a certain sense) than multivariate class-1 estimators.     

Flexible Multivariate Density Estimation With Marginal Adaptation

This article is concerned with multivariate density estimation. We discuss deficiencies in two popular multivariate density estimators—mixture and copula estimators, and propose a new class of estimators that combines the advantages of both mixture and copula modeling, while being more robust to their weaknesses. Our method adapts any multivariate density estimator using information obtained by separately estimating the marginals. We propose two marginally adapted estimators based on a multivariate mixture of normals and a mixture of factor analyzers estimators. These estimators are implemented using computationally efficient split-and-elimination variational Bayes algorithms. It is shown through simulation and real-data examples that the marginally adapted estimators are capable of improving on their original estimators and compare favorably with other existing methods. Supplementary materials for this article are available online.     

Simultaneous Estimation of Several Intraclass Correlation Coefficients

Based on shrinkage and preliminary test rules, various estimators are proposed for estimation of several intraclass correlation coefficients when independent samples are drawn from multivariate normal populations. It is demonstrated that the James-Stein type estimators are asymptotically superior to the usual estimators. Furthermore, it is also indicated through asymptotic results that none of the preliminary test and shrinkage estimators dominate each other, though they perform relatively well as compared to the classical estimator. The relative dominance picture of the estimators is presented. A Monte Carlo study is performed to appraise the properties of the proposed estimators for small samples.     

混合模型中方差分量估计的容许性及非负估计

对含有两个方差分量的线性混合模型, 本文构造了方差分量的一个线性估计类, 它包含许多常见的方差分量估计. 在这个类中我们建立了容许性的必要条件, 据此得到了两个新的改进估计. 最后我们讨论了方差分量的非负估计, 得到了优于方差分析估计和Tatsuya估计的正估计.     

An improved Afriat–Diewert–Parkan nonparametric production function estimator

Recent developments in the production frontier literature include nonparametric estimators with shape constraints. A few of these estimators rely on the Afriat inequalities to provide piecewise linear approximations to the production function/frontier. We show in this paper that these Afriat–Diewert–Parkan (ADP) estimators have deficiencies in the presence of moderate statistical noise including overfitting and a relatively high estimator variance. We propose new estimators with lower variance and a relatively low bias. We consider such alternative estimators based on (weighted) averages of random hinge functions with parameter restrictions. Small sample properties of the estimators are presented that show our new estimators outperform the existing ADP estimators when moderate to large amounts of noise are present.     

Estimating hazard ratios in nested case-control studies by mantel-haenszel method

1. IntroductionConsider a follow-up study which is carried out to investigate the association betweenexposure variables and mortality rate in a cohort. In the case where the cohort is of 1argesise, the complete follow-up ndght be too expensive or difficult, and various nested samplingmethod8 have been suggested by Thomas[l], Prenti..[2] 5 Goldstein and Langholzl'] and otherauthors. Most of the authors employ Coxl4] regression mode1 for estimating the hazard ratio8of exposures.Now a well-reco…     

Robust weighted orthogonal regression in the errors-in-variables model

This paper focuses on robust estimation in the structural errors-in-variables (EV) model. A new class of robust estimators, called weighted orthogonal regression estimators, is introduced. Robust estimators of the parameters of the EV model are simply derived from robust estimators of multivariate location and scatter such as the M-estimators, the S-estimators and the MCD estimator. The influence functions of the proposed estimators are calculated and shown to be bounded. Moreover, we derive the asymptotic distributions of the estimators and illustrate the results on simulated examples and on a real-data set.     

Bayesian inference using record values from Rayleigh model with application

In this article, based on a set of upper record values from a Rayleigh distribution, Bayesian and non-Bayesian approaches have been used to obtain the estimators of the parameter, and some lifetime parameters such as the reliability and hazard functions. Bayes estimators have been developed under symmetric (squared error) and asymmetric (LINEX and general entropy (GE)) loss functions. These estimators are derived using the informative and non-informative prior distributions for σ. We compare the performance of the presented Bayes estimators with known, non-Bayesian, estimators such as the maximum likelihood (ML) and the best linear unbiased (BLU) estimators. We show that Bayes estimators under the asymmetric loss functions are superior to both the ML and BLU estimators. The highest posterior density (HPD) intervals for the Rayleigh parameter and its reliability and hazard functions are presented. Also, Bayesian prediction intervals of the future record values are obtained and discussed. Finally, practical examples using real record values are given to illustrate the application of the results.     

Robustness of Stein-type estimators under a non-scalar error covariance structure

The Stein-rule (SR) and positive-part Stein-rule (PSR) estimators are two popular shrinkage techniques used in linear regression, yet very little is known about the robustness of these estimators to the disturbances’ deviation from the white noise assumption. Recent studies have shown that the OLS estimator is quite robust, but whether this is so for the SR and PSR estimators is less clear as these estimators also depend on the F statistic which is highly susceptible to covariance misspecification. This study attempts to evaluate the effects of misspecifying the disturbances as white noise on the SR and PSR estimators by a sensitivity analysis. Sensitivity statistics of the SR and PSR estimators are derived and their properties are analyzed. We find that the sensitivity statistics of these estimators exhibit very similar properties and both estimators are extremely robust to MA(1) disturbances and reasonably robust to AR(1) disturbances except for the cases of severe autocorrelation. The results are useful in light of the rising interest of the SR and PSR techniques in the applied literature.     

Assessing the performance of empirical bayes estimators

Methods for deriving empirical Bayes estimators are generally available. Corresponding general techniques for assessing the performance of these estimators are not widely developed yet, however. In this paper we provide a general procedure for assessing and comparing the performance of the empirical Bayes estimators and other estimators in a given data set.     

Quantile estimation under successive sampling

This paper deals with the estimation, under sampling in two successive occasions, of a finite population quantile. For this sampling design a class of estimators is proposed whose the ratio and difference estimators are particular cases. Asymptotic variance formulae are derived for the proposed estimators, and the optimal matching fraction is discussed. Comparisons are made with existing estimators in a simulation study using a natural population.     

Optimal convergence rates and asymptotic efficiency of point estimators under truncated distribution families

For regular and irregular truncated distribution families, the optimal convergence rates of consistent point estimators have been found and the corresponding asymptotic efficiencies established. Also, it has been justified that commonly used estimators are all efficient. The efficiencies here are compared to the efficiencies of asymptotically median unbiased estimators, providing a lot of counter estimator examples such that those estimators are efficient in the former sense, but not in the latter.     

广义偏最小二乘(PLS)估计类

本文研究了一类含有偏最小二乘（partialleastsquaresPLS）估计的估计类．给出了PLS估计的一般代数形式；讨论了含有PLS估计的广义PPLS估计类的统计性质；给出了该估计类优于最小二乘估计的条件．     

Estimating parameters in one-way analysis of covariance model with short-tailed symmetric error distributions

We consider one-way analysis of covariance (ANCOVA) model with a single covariate when the distribution of error terms are short-tailed symmetric. The maximum likelihood (ML) estimators of the parameters are intractable. We, therefore, employ a simple method known as modified maximum likelihood (MML) to derive the estimators of the model parameters. The method is based on linearization of the intractable terms in likelihood equations. Incorporating these linearizations in the maximum likelihood, we get the modified likelihood equations. Then the MML estimators which are the solutions of these modified equations are obtained. Computer simulations were performed to investigate the efficiencies of the proposed estimators. The simulation results show that the proposed estimators are remarkably efficient compared with the conventional least squares (LS) estimators.     

基于价格极值构建有效价差的广义矩估计

基于Corwin和Schultz(2012)提出的有效价差的High-Low估计,结合价格极值信息得到新的一阶矩条件,构造了有效价差的广义矩估计。随后通过随机数值模拟比较了基于价格极值的广义矩估计(GMM)与Roll的协方差估计、Bayes估计以及Corwin和Schultz的High-Low估计在多种不同状态下的估计精度。数值模拟结果显示,无论在交易连续的理想状态下还是交易不连续且波动率相对不高的非理想状态下,GMM估计的精度均高于其余三种估计;基于我国股票市场的实例分析,也表明GMM估计的估计精度优于其余三种估计。因此,GMM估计为度量金融资产的交易成本提供了一种有效方法。     

Asymptotic representations for importance-sampling estimators of value-at-risk and conditional value-at-risk

Value-at-risk (VaR) and conditional value-at-risk (CVaR) are important risk measures. They are often estimated by using importance-sampling (IS) techniques. In this paper, we derive the asymptotic representations for IS estimators of VaR and CVaR. Based on these representations, we are able to prove the consistency and asymptotic normality of the estimators and to provide simple conditions under which the IS estimators have smaller asymptotic variances than the ordinary Monte Carlo estimators.     

Rates of convergence for minimum contrast estimators

Summary We shall present here a general study of minimum contrast estimators in a nonparametric setting (although our results are also valid in the classical parametric case) for independent observations. These estimators include many of the most popular estimators in various situations such as maximum likelihood estimators, least squares and other estimators of the regression function, estimators for mixture models or deconvolution... The main theorem relates the rate of convergence of those estimators to the entropy structure of the space of parameters. Optimal rates depending on entropy conditions are already known, at least for some of the models involved, and they agree with what we get for minimum contrast estimators as long as the entropy counts are not too large. But, under some circumstances (large entropies or changes in the entropy structure due to local perturbations), the resulting the rates are only suboptimal. Counterexamples are constructed which show that the phenomenon is real for non-parametric maximum likelihood or regression. This proves that, under purely metric assumptions, our theorem is optimal and that minimum contrast estimators happen to be suboptimal.