On a differential equation approach to the weighted orthogonal Procrustes problem

The weighted orthogonal Procrustes problem, an important class of data matching problems in multivariate data analysis, is reconsidered in this paper. It is shown that a steepest descent flow on the manifold of orthogonal matrices can naturally be formulated. This formulation has two important implications: that the weighted orthogonal Procrustes problem can be solved as an initial value problem by any available numerical integrator and that the first order and the second order optimality conditions can also be derived. The proposed approach is illustrated by numerical examples.     

A note on optimal vector unbiased predictor

A characterization of optimal vector unbiased predictor is obtained. Some properties of optimal unbiased predictors are established. It is shown that simultaneous prediction of future random variables is equivalent to marginal prediction of these random variables. Following Kale and Chandrasekar (1983) and Chandrasekar (1984), it is shown that the criteria proposed by ishii (1969) based on matrices and the one proposed by Bibby and Toutenburg (1977) based on quadratic loss in the class of vector unbiased predictors are equivalent. The above approach is illustrated with some examples.     

Selection of error probability laws by generalized modified profile likelihood

Although error probability law selection of models of location-scale forms is of importance in some sense, the commonly used model selection procedures, such as AIC and BIC, do not apply to it. By treating error probability law as a “parameter” of interest, location and scale as nuisance parameters, this paper proposes that generalized modified profile likelihood (GMPL), considered as a quasi-likelihood function of error probability law, be used to select the error probability laws. The GMPL method achieves minimax rate optimality and proves to be consistent. Simulations show its good performance for finite and even small samples. Note that it is straightforward to generalize the GMPL of location-scale models to various models of location-scale forms particularly including the various linear regression models and their variations, to select their error probability laws. The author believes that GMPL and its variations would be quite promising for various model selection problems.     

Distributed Decision‐Making in Supply Chains and Private E‐Marketplaces

This paper develops a distributed decision‐making framework for the players in a supply chain or a private e‐marketplace to collaboratively arrive at a global Pareto‐optimal solution. In this model, no player has complete knowledge about all the costs and constraints of the other players. The decision‐making framework employs an iterative procedure, based on the Integer L‐shaped method, in which a master problem is solved to propose global solutions, and each player uses his local problems to construct feasibility and optimality cuts on the master problem. The master problem is modeled as a mixed‐integer program, and the players' local problems are formulated as linear programs. Collaborative planning scenarios in private e‐marketplaces and in supply chains were formulated and solved for test data. The results show that this distributed model is able to achieve near‐optimal solutions considerably faster than the traditional centralized approach.     

Empirical Bayes testing for guarantee lifetime: Non identical components case

This article considers an empirical Bayes testing problem for the guarantee lifetime in the two-parameter exponential distributions with non identical components. We study a method of constructing empirical Bayes tests under a class of unknown prior distributions for the sequence of the component testing problems. The asymptotic optimality of the sequence of empirical Bayes tests is studied. Under certain regularity conditions on the prior distributions, it is shown that the sequence of the constructed empirical Bayes tests is asymptotically optimal, and the associated sequence of regrets converges to zero at a rate O(n^{? 1 + 1/[2(r + α) + 1]}) for some integer r ? 0 and 0 ? α ? 1 depending on the unknown prior distributions, where n is the number of past data available when the (n + 1)st component testing problem is considered.     

Optimal designs for minimising covariances among parameter estimators in a linear model

We construct approximate optimal designs for minimising absolute covariances between least‐squares estimators of the parameters (or linear functions of the parameters) of a linear model, thereby rendering relevant parameter estimators approximately uncorrelated with each other. In particular, we consider first the case of the covariance between two linear combinations. We also consider the case of two such covariances. For this we first set up a compound optimisation problem which we transform to one of maximising two functions of the design weights simultaneously. The approaches are formulated for a general regression model and are explored through some examples including one practical problem arising in chemistry.     

关于社会主义新农村建设的经济理论基础探析

社会主义新农村建设正在迅猛向前推进，其经济理论基础是什么？本文通过分析认为：可持续发展理论指导了社会主义新农村建设的目标定位，平衡发展理论和帕累托最优理论指引和校正了社会主义新农村发建设的行动，它们共同形成了社会主义新农村建设的理论基础，支撑和引领社会主义新农村建设稳步向前发展。     

Optimal balanced block designs for correlated observations

The construction of universally optimal designs, if such exist, is difficult to obtain, especially when there are some nuisance effects or correlated errors. The hub correlation is a special correlation structure with applications to experiments in genetics, networks and other areas in industry and agriculture. There may be restrictions on the correlation values of the hub structure depending on the experiment. Optimality of block designs under hub correlation has been studied for the case of a constant correlation value. In this article, we consider the hub structure when one of the correlation values is different from the others, and the universally optimal block designs, binary or non-binary, are theoretically obtained. Also, we introduce an algorithm to construct the optimal designs. The Canadian Journal of Statistics 48: 596–604; 2020 © 2020 Statistical Society of Canada     

GIPSCAL revisited. A projected gradient approach

A model for analysis and visualization of asymmetric data—GIPSCAL—is reconsidered by means of the projected gradient approach. GIPSCAL problem is formulated as initial value problem for certain first order matrix ordinary differential equations. This results in a globally convergent algorithm for solving GIPSCAL. Additionally, first and second order optimality conditions for the solutions are established. A generalization of the GIPSCAL model for analyzing three-way arrays is also considered. Finally, results from simulation experiments are reported.     

A relaxation procedure for calculating (G–)minimax optimal designs

Summary: In nonlinear statistical models, standard optimality functions for experimental designs depend on the unknown parameters of the model. An appealing and robust concept for choosing a design is the minimax criterion. However, so far, minimax optimal designs have been calculated efficiently under various restrictive conditions only. We extend an iterative relaxation scheme originally proposed by Shimizu and Aiyoshi (1980) and prove its convergence under very general assumptions which cover a variety of situations considered in experimental design. Application to different specific design criteria is discussed and issues of practical implementation are addressed. First numerical results suggest that the method may be very efficient with respect to the number of iterations required.*Supported by a grant from the Deutsche Forschungsgemeinschaft. We are grateful to a referee for his constructive suggestions.