On invariant parametric covariance families

Summary In this note we characterize all linear transformations of random vectors which are invariant for a given parametric covariance family. Two one-dimensional covariance families are discussed in detail.     

Minimax estimation of constrained parametric functions for discrete families of distributions

For a vast class of discrete model families where the natural parameter is constrained to an interval, we give conditions for which the Bayes estimator with respect to a boundary supported prior is minimax under squared error loss type functions. Building on a general development of éric Marchand and Ahmad Parsian, applicable to squared error loss, we obtain extensions to various parametric functions and squared error loss type functions. We provide illustrations for various distributions and parametric functions, and these include examples for many common discrete distributions, as well as when the parametric function is a zero-count probability, an odds-ratio, a Binomial variance, and a Negative Binomial variance, among others. The Research of M. Jafari Jozani is supported by a grant of the Institute for Research and Planning in Higher Education, Ministry of Science, Research and Technology, Iran. The Research of é. Marchand is supported by NSERC of Canada.     

On equalities of estimations of parametric functions under a general linear model and its restricted models

Estimations of parametric functions under a general linear model and its restricted models involve some complicated operations of matrices and their generalized inverses. In the past several years, a powerful tool—the matrix rank method was utilized to manipulate various complicated matrix expressions that involve generalized inverses of matrices. In this paper, we use this method to derive necessary and sufficient conditions for six equalities of the ordinary least-squares estimators and the best linear unbiased estimators of parametric functions to equal under a general linear model and its corresponding restricted model.     

Nonparametric estimation of conditional distribution functions with longitudinal data and time-varying parametric models

Nonparametric estimation and inferences of conditional distribution functions with longitudinal data have important applications in biomedical studies. We propose in this paper an estimation approach based on time-varying parametric models. Our model assumes that the conditional distribution of the outcome variable at each given time point can be approximated by a parametric model, but the parameters are smooth functions of time. Our estimation is based on a two-step smoothing method, in which we first obtain the raw estimators of the conditional distribution functions at a set of disjoint time points, and then compute the final estimators at any time by smoothing the raw estimators. Asymptotic properties, including the asymptotic biases, variances and mean squared errors, are derived for the local polynomial smoothed estimators. Applicability of our two-step estimation method is demonstrated through a large epidemiological study of childhood growth and blood pressure. Finite sample properties of our procedures are investigated through simulation study.     

On continuous utility functions derived from demand functions

In the theory of revealed preference and in the approach to integrability theory of Hurwicz and Uzawa certain conditions are proposed implying the existence of a utility function generating the given demand function. This article presents a hypothesis which, under supposition of some well-known axioms of those models, is necessary and sufficient for the existence of a continuous utility function. This hypothesis implies the existence of a utility function u with the property that all of the boundary points of the set $\text{{x|u(x)≧α}}$ for every $\text{α?}\text{R}$ are lower boundary points, being fundamental for the continuity of the utility function.     

On intermediate utility functions

Intermediate utility functions have been recently introduced by Persson and Tabellini (2000, Political Economics: Explaining Economics Policy, MIT Press, Cambridge) and ensure the existence of a majority voting equilibrium at multi-dimensional voting. Here, we show that monotone transforms of these utility functions also are sufficient for the existence of a Condorcet winner.     

On the evaluation of poly-t density functions

Poly-t densities are defined by the property that their kernel is a product, or a ratio of products, of multivariate t-density kernels. As discussed in Drèze (1977), these densities arise as Bayesian posterior densities for regression coefficients under a variety of specifications for the prior density and the data generating process. We have therefore developed methods and computer algorithms to evaluate integrating constants and other characteristics of poly-t densities with no more than a single quadratic form in the numerator (section 2). As a by-product of our analysis we have also derived an algorithm for the computation of moments of positive definite quadratic forms in Normal variables (section 3). In section 4 we discuss inference on the sampling variances associated with the models discussed in Drèze (1977).     

On the continuity of representations of effectivity functions

An effectivity function assigns to each coalition of individuals in a society a family of subsets of alternatives such that the coalition can force the outcome of society’s choice to be a member of each of the subsets separately. A representation of an effectivity function is a game form with the same power structure as that specified by the effectivity function. In the present paper we investigate the continuity properties of the outcome functions of such representation. It is shown that while it is not in general possible to find continuous representations, there are important subfamilies of effectivity functions for which continuous representations exist. Moreover, it is found that in the study of continuous representations one may practically restrict attention to effectivity functions on the Cantor set. Here it is found that general effectivity functions have representations with lower or upper semicontinuous outcome function.     

会展业的发展与城市的能性、能级及能位

城市会展业与城市功能之间存在着密切的联系。从城市会展业与城市功能动态演变的角度,分析了两者在不同历史发展阶段的主要特征。研究显示,城市会展业与城市功能的关联机理从理念层面、互动层面和具体层面分别表现为适配关系、互动关系和耦合关系。     

On the impatience implications of Paretian social welfare functions

In this paper, we investigate the impatience implications resulting from the assumption of existence of a Paretian social welfare function (SWF) aggregating infinite utility streams. We show, for very general program spaces, that the set of utility streams, at which the SWF exhibits impatience, has the power of the continuum. In the context of a more special program space, which has figured prominently in the literature, we establish that this set is dense, so that even if there is a point in the program space at which the SWF does not exhibit impatience, there are points close to it at which it does. If the Paretian SWF is continuous (in the sup metric), we show that impatience is generic: the collection of points, at which the SWF does not exhibit impatience, is a closed, nowhere dense set.     

北京城市功能综合化的深层原因

政治中心是北京发展的决定性因素.在北京发展战略研究中,人口规模和建设规模是两大难题,规划指标反复被突破,原因是对政治中心的强大后续效应估计不足,对政治中心城市功能综合化估计不足.政治中心有直接后续效应,也有通过制度、文化、心理等因素延伸的间接后续效应.间接后续效应是城市发展的超经济动力.     

On the approximation of utility functions for faculty teaching assignments

A number of mathematical programming models have been proposed for generating faculty teaching assignments. Usually these models attempt to maximize the sum of the faculty members' utilities for the courses in the assignments. This paper demonstrates that the use of course utilities ignores important interaction effects in the determination of a faculty member's utility for a teaching schedule. As a result, solutions generated by the models can be far from optimal if the true objective of the scheduler is to maximize faculty utilities for their teaching schedules.