Concentration behavior of the penalized least squares estimator

Consider the standard nonparametric regression model and take as estimator the penalized least squares function. In this article, we study the trade‐off between closeness to the true function and complexity penalization of the estimator, where complexity is described by a seminorm on a class of functions. First, we present an exponential concentration inequality revealing the concentration behavior of the trade‐off of the penalized least squares estimator around a nonrandom quantity, where such quantity depends on the problem under consideration. Then, under some conditions and for the proper choice of the tuning parameter, we obtain bounds for this nonrandom quantity. We illustrate our results with some examples that include the smoothing splines estimator.     

Consistent estimation in the bilinear multivariate errors-in-variables model

A bilinear multivariate errors-in-variables model is considered. It corresponds to an overdetermined set of linear equations AXB=C, A∈ℝ^m×n, B∈ℝ^p×q, in which the data A, B, C are perturbed by errors. The total least squares estimator is inconsistent in this case.  An adjusted least squares estimator is constructed, which converges to the true value X, as m →∞, q →∞. A small sample modification of the estimator is presented, which is more stable for small m and q and is asymptotically equivalent to the adjusted least squares estimator. The theoretical results are confirmed by a simulation study. Acknowledgements. We thank two anonymous reviewers for their suggestions and corrections.? A. Kukush is supported by a postdoctoral research fellowship of the Belgian office for Scientific, Technical and Cultural Affairs, promoting Scientific and Technical Collaboration with Central and Eastern Europe.? S. Van Huffel is a full professor with the Katholieke Universiteit Leuven.? I. Markovsky is a research assistant with the Katholieke Universiteit Leuven.? This paper presents research results of the Belgian Programme on Interuniversity Poles of Attraction (IUAP V-22), initiated by the Belgian State, Prime Minister's Office – Federal Office for Scientific, Technical and Cultural Affairs of the Concerted Research Action (GOA) projects of the Flemish Government MEFISTO-666 (Mathematical Engineering for Information and Communication Systems Technology), of the IDO/99/03 project (K.U. Leuven) “Predictive computer models for medical classification problems using patient data and expert knowledge”, of the FWO projects G.0078.01, G.0200.00, and G0.0270.02.? The scientific responsibility is assumed by its authors.     

Pitfalls of Normal-Gamma Stochastic Frontier Models

Although conceptually pleasing, normal-gamma frontier models lead to difficult estimation problems. It is shown here that unless the sample size reaches several thousands of observations the shape parameter of the gamma density is hard to estimate, and that this carries over to estimates of the stochastic frontier, the individual inefficiencies, and the allocation of the overall variance to the stochastic frontier and to the inefficiencies.     

基于径向基神经网络的物流绩效评价方法

在分析物流绩效关键影响因素基础上,提出采用径向基神经网络模型应用于物流绩效评价测试。以多个主要影响因子为网络的输入信息,建立物流绩效综评遗传神经网络模型,采用正交最小二乘法进行学习训练,进行不同综合评价方法对比。     

The differing roles of success drivers across sequential channels: An application to the motion picture industry

In several product categories, it is typical to release products sequentially to different markets and customer segments. Conventional knowledge holds that the roles of various product success drivers do not differ significantly across these sequential channels of distribution. The authors examine sequential distribution channels within the motion picture industry and develop a model that proposes that such differences exist between a primary (short- and long-term theatrical box office) and a sequential (video rental) channel. The authors test their model with a sample of 331 motion pictures released in theaters and on video during 1999–2001 using partial least squares. Results reveal differences in the impact of success factors across channels. For example, cultural familiarity enhances box office success but relates negatively to video rental success, and distribution intensity and date of release enhance box office outcomes but have no impact on rental revenues. Thorsten Hennig-Thurau (tht@medien.uni-weimar.cie) is a professor of marketing and media research at Bauhaus-University of Weimar’s Media School and Honorary Visiting Professor of Movie Marketing in the Faculty of Management of Cass Business School, City University London. He has published articles in theJournal of Marketing, theJournal of Service Research, theInternational Journal of Electronic Commerce, theJournal of Interactive Marketing, Psychology & Marketing, and theJournal of Consumer Affairs, among others. He is author of the monograph Relationship Marketing, which has been translated into Chinese. He is member of the editorial board of three journals and serves as reviewer for theJournal of Marketing andMarketing Science. He has won eight Best Article and Best Paper Awards, including the Overall Best Paper Award of the 2005 American Marketing Association Summer Educators’ Conference and the 2002JSR Excellence in Service Research Award. Mark B. Houston (houstonmb@missouri.edu) (PhD, Arizona State University) is the David and Judy O’Neal MBA Professor at the University of Missouri-Columbia. His research on strategy, interfirm relationships, and innovation has been published in leading journals, including theJournal of Marketing, theJournal of Marketing Research, theJournal of Consumer Research, Marketing Science, theJournal of the Academy of Marketing Science, and theJournal of Financial and Quantitative Analysis. He cochaired the 2005 American Marketing Association (AMA) Summer Educators’ Conference and served for two terms as vice president of the AMA’s Technology and Marketing Special Interest Group. Gianfranco Walsh (g.walsh@strath.ac.uk) received his MPhil degree from UMIST (England) and PhD (2001) and Habilitation (2004) degrees from Hanover (Germany). His research focuses on consumer behavior, corporate reputation, and e-commerce. He has presented numerous papers at international conferences. His work has been published in, among others, theAcademy of Marketing Science Review, the International Journal of Electronic Commerce, theJournal of Consumer Affairs, theJournal of Interactive Marketing, theJournal of Macromarketing, and theJournal of Marketing Management. He is the Chair of Marketing and Electronic Retailing at the Institute for Management, University of Koblenz-Landau.     

基于应变数线性变换的约束广义G-M估计

考虑线性变换对约束线性模型回归系数的影响问题，证明了观测数据的线性变换对于约束模型的影响可以通过一个可用两步约束最小二乘法解决的约束回归问题进行了分析，得到了回归系数的约束可估函数的约束最佳线尾无偏估计不受变换影响的充要条件。     

Subjective recursive expected utility

We axiomatize a subjective version of the recursive expected utility model. This development extends the seminal results of Kreps and Porteus (Econometrica 46:185–200 (1978)) to a subjective framework and provides foundations that are easy to relate to axioms familiar from timeless models of decision making under uncertainty. Our analysis also clarifies what is needed in going from a represention that applies within a single filtration to an across filtration representation.Part of this research was conducted when Ozdenoren visited MEDS in Fall 2003. We thank Tapas Kundu, Costis Skiadas, Jean-Marc Tallon and Tan Wang for helpful discussions and also thank audiences at Koc University, Northwestern University, the CERMSEM conference “ Mathematical Models in Decision Theory” at Universite Paris I, and the FUR XI conference on foundations and applications of utility, risk and decision theory     

The convergence of least squares learning in stochastic temporary equilibrium models

Summary. This paper provides conditions for the almost sure convergence of the least squares learning rule in a stochastic temporary equilibrium model, where regressions are performed on the past values of the endogenous state variable. In contrast to earlier studies, (Evans and Honkapohja, 1998; Marcent and Sargent, 1989), which were local analyses, the dynamics are studied from a global viewpoint, which allows one to obtain an almost sure convergence result without employing projection facilities. Received: April 7, 2001; revised version: September 5, 2001     

基于LINGO的最小一乘线性回归的参数估计

采用最小二乘法进行回归分析,容易受到奇异点的影响;最小一乘法虽能很好地克服这一缺陷,但又存在计算困难.利用LINGO软件能够快速、准确地估计出最小一乘线性回归的参数,从而使其成为一种有效的参数估计方法.     

Recursive utility with unbounded aggregators

A new framework is presented for the study of the existence and uniqueness of solutions to the Koopmans’ equation in the unbounded case, that is based on the contraction mapping approach. In the bounded below case with bounded consumption streams, uniqueness of the solution in the whole class of weak-star continuous utility functions is obtained. When the aggregator is unbounded below and/or consumption streams are unbounded, existence of a weak-star continuous solution is shown, and a simple criterium to check the sufficient conditions for existence is provided. Juan Pablo Rincón-Zapatero and Carlos Rodríguez-Palmero gratefully acknowledge financial support by the Ministerio de Educación y Ciencia and FEDER funds under Research Projects MTM2005-06534 and SEJ2005-08709/ECON, respectively, and by Consejería de Educación de la Junta de Castilla y León under Research Projects VA99/04 and VA017B05, respectively. This paper has substantially benefited from the comments of an anonymous referee. Particular and special thanks are due to Robert Becker for his very helpful comments and valuable suggestions.