Restricted minimax estimation in semiparametric linear models

Abstract

In this article we develop the minimax estimation approach of general linear models to the semiparametric linear models when the parameters are simultaneously constrained by an ellipsoid and linear restrictions. Combining sample information and prior constraints the minimax estimator is obtained and compared with partially least square estimator by theoretical and simulation methods.     

On Optimality of Bayesian Wavelet Estimators

Abstract.  We investigate the asymptotic optimality of several Bayesian wavelet estimators, namely, posterior mean, posterior median and Bayes Factor, where the prior imposed on wavelet coefficients is a mixture of a mass function at zero and a Gaussian density. We show that in terms of the mean squared error, for the properly chosen hyperparameters of the prior, all the three resulting Bayesian wavelet estimators achieve optimal minimax rates within any prescribed Besov space     for p  ≥ 2. For 1 ≤  p  < 2, the Bayes Factor is still optimal for (2 s +2)/(2 s +1) ≤  p  < 2 and always outperforms the posterior mean and the posterior median that can achieve only the best possible rates for linear estimators in this case.     

Deconvolution with supersmooth distributions

Nonparametric deconvolution problems require one to recover an unknown density when the data are contaminated with errors. Optimal global rates of convergence are found under the weighted L_p-loss (1 ≤ p ≤ ∞). It appears that the optimal rates of convergence are extremely low for supersmooth error distributions. To resolve this difficulty, we examine how high the noise level can be for deconvolution to be feasible, and for the deconvolution estimate to be as good as the ordinary density estimate. It is shown that if the noise level is not too high, nonparametric Gaussian deconvolution can still be practical. Several simulation studies are also presented.     

Treatment Choice With Trial Data: Statistical Decision Theory Should Supplant Hypothesis Testing

Abstract

A central objective of empirical research on treatment response is to inform treatment choice. Unfortunately, researchers commonly use concepts of statistical inference whose foundations are distant from the problem of treatment choice. It has been particularly common to use hypothesis tests to compare treatments. Wald’s development of statistical decision theory provides a coherent frequentist framework for use of sample data on treatment response to make treatment decisions. A body of recent research applies statistical decision theory to characterize uniformly satisfactory treatment choices, in the sense of maximum loss relative to optimal decisions (also known as maximum regret). This article describes the basic ideas and findings, which provide an appealing practical alternative to use of hypothesis tests. For simplicity, the article focuses on medical treatment with evidence from classical randomized clinical trials. The ideas apply generally, encompassing use of observational data and treatment choice in nonmedical contexts.     

On the construction of optimal experimental designs: a penalty approach

Tn optimal experimental design theory there are well-known situations, in which additional constraints are implied to the design set. These constraints destroy in general the simplex structure of the set of feasible points of the design set. Thus the available iteration procedures for the unrestricted case are no longer applicable.

In this paper a penalty approach is suggested which transforms the restricted problem to the unrestricted case and allows the application of well-known algorithms such as the Fedorov-Wynn-type or the projected gradient procedure.     

Minimax property of stein's estimator

Stein's estimator and some other estimators of the mean of a K-variate normal distribution are known to dominate the maximum likelihood estimator under quadratic loss for K > 3, and are therefore minimax. In this paper it is shown that the minimax property of Stein's rule is preserved with respect to a generalized loss function.     

损失厌恶、后悔厌恶与沉没成本效应的关联性分析

以往研究认为沉没成本效应的产生与损失厌恶和后悔厌恶相关,但对其相互关系的探讨较少考虑货币性沉没成本和非货币性沉没成本的不同影响.文章选取证券监管者和证券市场投资者作为被试对象,通过有情境因素的调查问卷对损失厌恶、后悔厌恶与沉没成本效应之间的关联性进行验证.实证结果发现,与证券市场投资者相比,证券监管者的损失厌恶倾向要显著更低,而二者的后悔厌恶和沉没成本效应则无显著差异;证券监管者的数据结果表明,后悔厌恶与沉没成本效应之间存在显著的相关性,而损失厌恶与沉没成本效应之间不存在显著的相关性;相比之下,证券市场投资者的数据结果则表明,损失厌恶与沉没成本之间存在显著的相关性,而后悔厌恶与沉没成本之间则不存在显著的相关性.     

女大学生在情绪后悔下择偶决策的信息加工方式

以42名20-26岁之间的某高校未婚女大学生为被试,采用诱发情绪后使用信息板进行择偶决策的方式探讨了她们在后悔情绪下择偶决策的信息加工方式。结果表明：（1）用影片和自由想象的方式能够诱发被试的后悔情绪;（2）无论情绪类型,时间限制和候选人数量均影响被试择偶决策的信息加工方式;（3）情绪类型即后悔情绪与中性情绪,对女大学生择偶决策的信息加工方式无显著影响。     

基于ART及多风险规避的交通网络均衡模型

随着对交通系统不确定性认识的深入,以绝对理性为基础的“期望效用理论”在风险环境下的路径选择分析中显示出局限性,而“预期后悔理论”则为之提供了新的分析思路.将预期后悔理论应用到风险环境下的路径选择分析中,将出行者一致风险规避的假设扩展到多风险规避,建立了基于后悔理论及多风险规避出行特征的交通网络随机用户均衡变分不等式模型,并给出了求解算法.通过算例分析发现,后悔心理对出行者的路径选择并不总是显著的.在非风险环境及极端风险环境中,后悔心理对出行者的路径选择影响是微弱的,但是当环境处于极端风险与非风险之间时,后悔心理对出行者路径选择有着较为显著的影响.     

Another look at Huber's estimator: A new minimax estimator in regression with stochastically bounded noise

Huber's estimator has had a long lasting impact, particularly on robust statistics. It is well known that under certain conditions, Huber's estimator is asymptotically minimax. A moderate generalization in rederiving Huber's estimator shows that Huber's estimator is not the only choice. We develop an alternative asymptotic minimax estimator and name it regression with stochastically bounded noise (RSBN). Simulations demonstrate that RSBN is slightly better in performance, although it is unclear how to justify such an improvement theoretically. We propose two numerical solutions: an iterative numerical solution, which is extremely easy to implement and is based on the proximal point method; and a solution by applying state-of-the-art nonlinear optimization software packages, e.g., SNOPT. Contribution: the generalization of the variational approach is interesting and should be useful in deriving other asymptotic minimax estimators in other problems.