On estimating domain totals over a subpopulation

A simple random sample is drawn over a finite population which is composed of several subpopulations. Each subpopulation consists several domains. The minimax estimator under squared error loss function for the domain totals over a subpopulation is derived, in which the number of sample units falling into the subpopulation is random.Supported by the General Research Fund of the University of Kansas.     

A family of minimax estimators of a multivariate normal mean

Let X be a p-dimensional normal random vector with unknown mean vector θ and covariance σ²I. Let S/σ², independent of X, be chi-square with n degrees of freedom. Relative to the squared error loss, James and Stein (1961) have obtained an estimator which dominates the usual estimator X. Baranchik (1970) has extended James and Stein's results. We obtain a theorem which can provide a different family of minimax estimators containing James-Stein's estimator. Two interesting minimax estimators are presented in this paper.     

A family of dominating minimax estimators of a multivariate normal mean

Let X have a p-variate normal distribution with mean vector θ and identity covariance matrix I. In the squared error estimation of θ, Baranchik (1970) gives a wide family G of minimax estimators. In this paper, a subfamily C of dominating estimators in G is found such that for each estimator δ₁ in G not in C, there exists an estimator δ₂ in C which which dominates δ₁.     

GAMMA－MINIMAX ESTIMATORS FOR THE MEAN OF A MULTIVARIATE NORMAL DISTRIBUTION WITH PARTIALLY UNKNOWN COVARIANCE MATRIX

ＧＡＭＭＡ－ＭＩＮＩＭＡＸＥＳＴＩＭＡＴＯＲＳＦＯＲＴＨＥＭＥＡＮＯＦＡＭＵＬＴＩＶＡＲＩＡＴＥＮＯＲＭＡＬＤＩＳＴＲＩＢＵＴＩＯＮＷＩＴＨＰＡＲＴＩＡＬＬＹＵＮＫＮＯＷＮＣＯＶＡＲＩＡＮＣＥＭＡＴＲＩＸＣＨＥＮＬＡＮＸＩＮＧ（陈兰祥）（Ｄｅｐａｒｔ...     

A novel two-phase group decision making approach for construction project selection in a fuzzy environment

This paper considers a construction project problem under multiple criteria in a fuzzy environment and proposes a new two-phase group decision making (GDM) approach. This approach integrates a modified analytic network process (ANP) and an improved compromise ranking method, known as VIKOR. To take uncertainty and risk into account, a new decision making approach is presented with multiple fuzzy information by a group of experts, and a risk attitude for each expert is incorporated that can be expressed linguistically. First, a modified fuzzy ANP method is introduced to address the problem of dependence as well as feedback among conflicting criteria and to determine their relative importance. Then, a fuzzy VIKOR method is extended to rank potential projects on the basis of their overall performance. An illustrative example from the literature is provided for the construction project problem to demonstrate the effectiveness and feasibility of the proposed approach. The computational results show that the proposed two-phase GDM approach is suitable to cope with imprecision and subjectivity for the complicated decision making problem. Finally, the associated results of the proposed approach with risk attitudes and without risk attitudes are compared with the results reported by Cheng and Li [1], and the merits are highlighted.     

Optimal scale selection for multi-scale decision tables

Human beings often observe objects or deal with data hierarchically structured at different levels of granulations. In this paper, we study optimal scale selection in multi-scale decision tables from the perspective of granular computation. A multi-scale information table is an attribute-value system in which each object under each attribute is represented by different scales at different levels of granulations having a granular information transformation from a finer to a coarser labelled value. The concept of multi-scale information tables in the context of rough sets is introduced. Lower and upper approximations with reference to different levels of granulations in multi-scale information tables are defined and their properties are examined. Optimal scale selection with various requirements in multi-scale decision tables with the standard rough set model and a dual probabilistic rough set model are discussed respectively. Relationships among different notions of optimal scales in multi-scale decision tables are further analyzed.     

Optimal selection of R&D projects

A model for the selection process of research and development (R&D) projects belonging to some common area and submitted to a funding agency is presented. Every project is evaluated, the result of this procedure providing the agency with some useful information about the distribution of the project's payoff. The uncertainty due to the unknown perspectives of the whole area of R&D is incorporated in a Bayesian way, so that the agency learns about the area value from the projects already handled. After specifying the model assumptions, adaptive dynamic programming techniques are applied to develop an optimal funding strategy for a given number of submitted projects. Some qualitative properties of the optimal strategy are derived, and the asymptotical behavior of the maximum expected reward is determined.     

带交易费的最优投资组合选择的极大极小方法

研究不允许卖空时不相关资产的最优投资选择问题.在风险资产收益率不能确切知道的情况下,建立了投资组合选择问题的极大极小模型.将交易费引入到极大极小模型中,交易费假定为新旧投资组合之差的V型函数.推导出有效投资组合与有效前沿的解析表达式.     

Linear Bayes and Optimal Estimation

In non-Bayesian statistics, it is often realistic to replace a full distributional assumption by a much weaker assumption about its first few moments; such as for instance, mean and variance. Along the same lines in Bayesian statistics one may wish to replace a completely specified prior distribution by an assumption about just a few moments of the distribution. To deal with such Bayesian semi-parametric models defined only by a few moments, Hartigan (1969, J. Roy. Statist. Soc. Ser. B, 31, 440-454) put forward linear Bayes methodology. By now it has become a standard tool in Bayesian analysis. In this paper we formulate an alternative methodology based on the theory of optimum estimating functions. This alternative methodology is shown to be more readily applicable and efficient in common problems, than the linear Bayes methodology mentioned above.     

Some topological minimax theorems

Two topological variants of the minimax theorem are proved with no restrictions on one of the spaces except for those related to the function under consideration. The conditions concerning the behavior of the function deal only with the interval between the maximin and minimax. As corollaries, we obtain the well-known theorems of Sion and Hoang-Tui on quasiconvex-quasiconcave semicontinuous functions. The scheme of arguments goes back to the Hahn-Banach theorem and the separating hyperplane theorem. It is shown how this scheme can be explicitly realized in the proof of the Hahn-Banach theorem. Translated fromMaternaticheskie Zametki, Vol. 67, No. 1, pp. 141–149, January, 2000.     

Optimal life-insurance selection and purchase within a market of several life-insurance providers

We consider the problem faced by a wage-earner with an uncertain lifetime having to reach decisions concerning consumption and life-insurance purchase, while investing his savings in a financial market comprised of one risk-free security and an arbitrary number of risky securities whose prices are determined by diffusive linear stochastic differential equations. We assume that life-insurance is continuously available for the wage-earner to buy from a market composed of a fixed number of life-insurance companies offering pairwise distinct life-insurance contracts. We characterize the optimal consumption, investment and life-insurance selection and purchase strategies for the wage-earner with an uncertain lifetime and whose goal is to maximize the expected utility obtained from his family consumption, from the size of the estate in the event of premature death, and from the size of the estate at the time of retirement. We use dynamic programming techniques to obtain an explicit solution in the case of discounted constant relative risk aversion (CRRA) utility functions.     

Portfolio selection for individual passive investing

This paper considers passive fund selection from an individual investor's perspective. The growth of the passive fund market over the past decade is staggering. Individual investors who wish to buy these funds for their retirement and brokerage accounts have many options and are faced with a difficult selection problem. Which funds do they invest in, and in what proportions? We develop a novel statistical methodology to address this problem by adapting recent advances in posterior summarization. A Bayesian decision‐theoretic approach is presented to construct optimal sparse portfolios for individual investors over time.     

On some multivariate density estimates and empirical Bayes problems

This paper consider estimates of multidimensional density functions and their derivatives. The asymptotic unbiasedness and the convergence properties of these estimates are established.Some applications to empirical Bayes problems are considered.     

A note on solving nonlinear minimax problems via a differentiable penalty function

The note demonstrates that modeling a nonlinear minimax problem as a nonlinear programming problem and applying a classical differentiable penalty function to attempt to solve the problem can lead to convergence to a stationary point of the penalty function which is not a feasible point of the nonlinear programming problem. This occurred naturally in an application from statistical reliability theory. The note resolves the problem through modification of both the problem formulation and the iterative penalty function method.     

ψ-correct decision for selection and elimination

Summary The selection oft out ofk populations with parameters θ _i (i=1, ...,k) is said to result in an ψ-correct decision provided ψ (minimum selected θ)>maximum non-selected θ where ψ(θ) (>θ) is an increasing function. For the cases of location or scale parameters the minimum probability of ψ-correct decision over the entire parameter space is shown to be no less than the minimum probability of correct selection over a preference zone determined by ψ(θ). For other types of parameters this result is shown to be true under certain conditions linking the distribution function and the ψ function.     

Optimal aggregation of fuzzy preference relations with an application to broadband internet service selection

This paper investigates the aggregation of multiple fuzzy preference relations into a collective fuzzy preference relation in fuzzy group decision analysis and proposes an optimization based aggregation approach to assess the relative importance weights of the multiple fuzzy preference relations. The proposed approach that is analytical in nature assesses the weights by minimizing the sum of squared distances between any two weighted fuzzy preference relations. Relevant theorems are offered in support of the proposed approach. Multiplicative preference relations are also incorporated into the approach using an appropriate transformation technique. An eigenvector method is introduced to derive the priorities from the collective fuzzy preference relation. The proposed aggregation approach is tested using two numerical examples. A third example involving broadband internet service selection is offered to illustrate that the proposed aggregation approach provides a simple, effective and practical way of aggregating multiple fuzzy preference relations in real-life situations.     

IPSSIS: An integrated multicriteria decision support system for equity portfolio construction and selection

A fundamental principle of modern portfolio theory is that comparisons between portfolios are generally made using two criteria, corresponding to the first two moments of return distributions, namely the expected return and portfolio variance. According to this model and according to most of the portfolio models derived from the stochastic dominance approach, the group of portfolios open to comparisons is divided into two parts: on the one hand there are the efficient portfolios (those that are not dominated by any other portfolio in the group), and on the other, those that are dominated. In other words, these models do not solve for one optimal portfolio, but rather solve for an efficient set of portfolios, among which the investor must choose, given his preference system. One criticism over these models, which has often been addressed both by practitioners and academics, is that they fail to embody the objectives of the decision maker (DM), through the various stages of the decision process. Our purpose in this article is to present an integrated and innovative methodological approach for the construction and selection of equity portfolios, which will take into account the inherent multidimensional nature of the problem, while allowing the DM to incorporate his preferences in the decision process. The proposed approach, which grounds its basis on the field of multiple criteria decision making (MCDM) and more specifically on multiobjective mathematical programming (MMP), is implemented in the IPSSIS (Integrated Portfolio Synthesis and Selection Information System) decision support system (DSS). The validity of the proposed approach is tested through an illustrative application in the Athens Stock Exchange (ASE).     

Quickest online selection of an increasing subsequence of specified size

Given a sequence of independent random variables with a common continuous distribution, we consider the online decision problem where one seeks to minimize the expected value of the time that is needed to complete the selection of a monotone increasing subsequence of a prespecified length n. This problem is dual to some online decision problems that have been considered earlier, and this dual problem has some notable advantages. In particular, the recursions and equations of optimality lead with relative ease to asymptotic formulas for mean and variance of the minimal selection time. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 49, 235–252, 2016