模糊集的无穷扩展原理

从普通集族{Xt}t?T（T为无限集）的直积Ⅱt?TXt出发，给出模糊集族At?F(Xt)(t?T)的直积概念；将通常的映射?：Ⅱt?TXt→Y扩展为模糊集族的直积Ⅱt?TF(Xt)到Y上的模糊集F(Y)的映射。     

A bayesian estimator for the dependence function of a bivariate extreme‐value distribution

Any continuous bivariate distribution can be expressed in terms of its margins and a unique copula. In the case of extreme‐value distributions, the copula is characterized by a dependence function while each margin depends on three parameters. The authors propose a Bayesian approach for the simultaneous estimation of the dependence function and the parameters defining the margins. They describe a nonparametric model for the dependence function and a reversible jump Markov chain Monte Carlo algorithm for the computation of the Bayesian estimator. They show through simulations that their estimator has a smaller mean integrated squared error than classical nonparametric estimators, especially in small samples. They illustrate their approach on a hydrological data set.     

关于参数化测度（Ⅱ）

引进一类拓扑向量空间，用以描述测度的偏导。使用的工具是所谓的参数化鞅。建立了若干参数化鞅的收敛定理。     

军机备件需求量修正的粗糙集方法

本文针对不可量化因素对军机备件需求量的影响,提出了基于粗糙集的备件需求量的修正方法。考虑不可量化因素存在多值性的问题,将不可分辨关系下的经典粗糙集方法拓展成相容关系下的扩展粗糙集方法,通过相容关系下的近似空间获取决策规则,再由决策规则得到修正系数。最后以轮胎类器材为例,说明了修正系数的获取过程。     

One-dimensional optimal bounded-shape partitions for Schur convex sum objective functions

Consider the problem of partitioning n nonnegative numbers into p parts, where part i can be assigned n_i numbers with n_i lying in a given range. The goal is to maximize a Schur convex function F whose ith argument is the sum of numbers assigned to part i. The shape of a partition is the vector consisting of the sizes of its parts, further, a shape (without referring to a particular partition) is a vector of nonnegative integers (n₁,..., n_p) which sum to n. A partition is called size-consecutive if there is a ranking of the parts which is consistent with their sizes, and all elements in a higher-ranked part exceed all elements in the lower-ranked part. We demonstrate that one can restrict attention to size-consecutive partitions with shapes that are nonmajorized, we study these shapes, bound their numbers and develop algorithms to enumerate them. Our study extends the analysis of a previous paper by Hwang and Rothblum which discussed the above problem assuming the existence of a majorizing shape. This research is partially supported by ROC National Science grant NSC 92-2115-M-009-014.     

Mixed integer (0–1) fractional programming for decision support in paper production industry

This paper presents an effective and efficient method for solving a special class of mixed integer fractional programming (FP) problems. We take a classical reformulation approach for continuous FP as a starting point and extend it for solving a more general class of mixed integer (0–1) fractional programming problems.To stress the practical relevance of the research we focus on a real-life application in paper production industry. The constantly advancing physical knowledge of large scale pulp and paper production did have a substantial impact on an existing DSS in which mixed integer (0–1) fractional programming is introduced. We show that the motivation to solve a real-life fractional programming problem can provide the basis for a new approach in a new context that has an added value of its own, even outside the given application area. We describe the main characteristics of the DSS, the necessity to develop a non-iterative solution procedure and demonstrate both the effectiveness and efficiency of the proposed approach from practical data sets.     

C14. Moments of the kolmogorov-smirnov one-sample statistic

In adaptive estimation, it is often considered that an estimator has made a mistake if the component estimator chosen for use is not the most efficient for the distribution sampled. Theoretical and simulation results point to a fallacy in this line of thought. The Monte Carlo study involves extension of the Princeton Swindle to distributions conditional on a location and scale-free statistic, and to the uniform. The results give a partial explanation for the sometimes surprising robustness of adaptive L-estimators.     

Improving TAIEX forecasting using fuzzy time series with Box–Cox power transformation

Box–Cox together with our newly proposed transformation were implemented in three different real world empirical problems to alleviate noisy and the volatility effect of them. Consequently, a new domain was constructed. Subsequently, universe of discourse for transformed data was established and an approach for calculating effective length of the intervals was then proposed. Considering the steps above, the initial forecasts were performed using frequently used fuzzy time series (FTS) methods on transformed data. Final forecasts were retrieved from initial forecasted values by proper inverse operation. Comparisons of the results demonstrate that the proposed method produced more accurate forecasts compared with existing FTS on original data.     

A Necessary Condition for the Strong Oracle Property

A problem of using a non‐convex penalty for sparse regression is that there are multiple local minima of the penalized sum of squared residuals, and it is not known which one is a good estimator. The aim of this paper is to give a guide to design a non‐convex penalty that has the strong oracle property. Here, the strong oracle property means that the oracle estimator is the unique local minimum of the objective function. We summarize three definitions of the oracle property – the global, weak and strong oracle properties. Then, we give sufficient conditions for the weak oracle property, which means that the oracle estimator becomes a local minimum. We give an example of non‐convex penalties that possess the weak oracle property but not the strong oracle property. Finally, we give a necessary condition for the strong oracle property.     

Model selection in high-dimensional noisy data: a simulation study

In many practical applications, high-dimensional regression analyses have to take into account measurement error in the covariates. It is thus necessary to extend regularization methods, that can handle the situation where the number of covariates p largely exceed the sample size n, to the case in which covariates are also mismeasured. A variety of methods are available in this context, but many of them rely on knowledge about the measurement error and the structure of its covariance matrix. In this paper, we set the goal to compare some of these methods, focusing on situations relevant for practical applications. In particular, we will evaluate these methods in setups in which the measurement error distribution and dependence structure are not known and have to be estimated from data. Our focus is on variable selection, and the evaluation is based on extensive simulations.