决策单调约简的启示

决策粗糙集模型源于贝叶斯决策准则,利用代价矩阵生成了构建概率粗糙集所需的一对阈值.但决策粗糙集并不具备经典粗糙集理论中常用的单调性,这给研究决策粗糙集的约简问题带来了机遇与挑战.通过考虑决策粗糙近似集是否变化,分析了决策粗糙集的决策保持约简与决策单调约简,并提出了两种不同的属性重要度以求解这两种约简.实验结果表明,相较于决策保持约简,通过决策单调约简,可以获得更多的由下近似与上近似所支持的决策规则,但同时也需付出更大的决策代价,从而揭示了想要得到更多,就必须付出更多的哲学道理.     

俄罗斯政坛出现三大趋势

最近,俄罗斯政坛出现三大趋势,一是强化国家政权,实行总统集权;二是改变政党格局,形成一党为主;三是规范民主生活,走向"可控民主".目前,普京总统集权的局面已经形成,令西方国家为之担忧.但这种情况符合俄罗斯的历史传统,符合俄重振大国地位的现实需要.由于时代条件已截然不同,俄罗斯不会再回到苏联时期和沙皇时期,普京的"集权"模式也不可能变成"极权"模式.     

Optimal Simultaneous Confidence Bands in Multiple Linear Regression with Predictor Variables Constrained in an Ellipsoidal Region

A simultaneous confidence band provides useful information on the plausible range of an unknown regression model function, just as a confidence interval gives the plausible range of an unknown parameter. For a multiple linear regression model, confidence bands of different shapes, such as the hyperbolic band and the constant width band, can be constructed and the predictor variable region over which a confidence band is constructed can take various forms. One interesting but unsolved problem is to find the optimal (shape) confidence band over an ellipsoidal region χ_E under the Minimum Volume Confidence Set (MVCS) criterion of Liu and Hayter (2007 Liu, W., Hayter, A.J. (2007). Minimum area confidence set optimality for confidence bands in simple linear regression. J. Amer. Statist. Assoc. 102:181–190.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) and Liu et al. (2009 Liu, W., Bretz, F., Hayter, A.J., Wynn, H.P. (2009). Assessing non-superiority, non-inferiority or equivalence when comparing two regression models over a restricted covariate region. Biometrics 65:1279–1287.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). This problem is challenging as it involves optimization over an unknown function that determines the shape of the confidence band over χ_E. As a step towards solving this difficult problem, in this paper, we introduce a family of confidence bands over χ_E, called the inner-hyperbolic bands, which includes the hyperbolic and constant-width bands as special cases. We then search for the optimal confidence band within this family under the MVCS criterion. The conclusion from this study is that the hyperbolic band is not optimal even within this family of inner-hyperbolic bands and so cannot be the overall optimal band. On the other hand, the constant width band can be optimal within the family of inner-hyperbolic bands when the region χ_E is small and so might be the overall optimal band.     

A nonparametric coherent confidence procedure

ABSTRACT

Holm's step-down testing procedure starts with the smallest p-value and sequentially screens larger p-values without any information on confidence intervals. This article changes the conventional step-down testing framework by presenting a nonparametric procedure that starts with the largest p-value and sequentially screens smaller p-values in a step-by-step manner to construct a set of simultaneous confidence sets. We use a partitioning approach to prove that the new procedure controls the simultaneous confidence level (thus strongly controlling the familywise error rate). Discernible features of the new stepwise procedure include consistency with individual inference, coherence, and confidence estimations for follow-up investigations. In a simple simulation study, the proposed procedure (treated as a testing procedure), is more powerful than Holm's procedure when the correlation coefficient is large, and vice versa when it is small. In the data analysis of a medical study, the new procedure is able to detect the efficacy of Aspirin as a cardiovascular prophylaxis in a nonparametric setting.     

Two new estimators of entropy for testing normality

ABSTRACT

We present two new estimators for estimating the entropy of absolutely continuous random variables. Some properties of them are considered, specifically consistency of the first is proved. The introduced estimators are compared with the existing entropy estimators. Also, we propose two new tests for normality based on the introduced entropy estimators and compare their powers with the powers of other tests for normality. The results show that the proposed estimators and test statistics perform very well in estimating entropy and testing normality. A real example is presented and analyzed.     

Some further aspects of the löwner-ordering antitonicity of the moore-penrose inverse

A survey is given of known proofs of the antitonicity of the inverse matrix function for positive definite matrices w.r.t. the Lowner partial ordering, and of the corresponding result for the Moore-Penrose inverse of nonnegative definite matrices [the theorem of Milliken and Akdeniz (1977)]. A short new proof of the latter result is obtained by employing an extremal representation of a nonnegative definite quadratic form. Another proof of this result involving Schur complements is also given, and is seen to be extendable to the case of symmetric (not necessarily nonnegative definite) matrices. A geometrical interpretation of Milliken and Akdeniz's theorem is presented. As an application, the relationship between the concepts of greater (maximum) concentration and smaller (minimum) dispersion is considered for a pair (class) of vector-valued statistics with possibly degenerate distributions.     

Reliability estimation based on ranked set sampling

In this paper we consider the problem of estimating the reliability of an exponential component based on a Ranked Set Sample (RSS) of size n. Given the first r observations of that sample, 1≤r≤n, we construct an unbiased estimator for this reliability and we show that these n unbiased estimators are the only ones in a certain class of estimators. The variances of some of these estimators are compared. By viewing the observations of the RSS of size n as the lifetimes of n independent k-out-of-n systems, 1≤k≤n, we are able to utilize known properties of these systems in conjunction with the powerful tools of majorization and Schur functions to derive our results.     

Formulas for stationary planar fibre processes III – intersections with fibre systems

In this paper we investigate the distribution of the periodogram, respectively, the periodogram matrix for stationary random sequences. These .distributions are consid¬ered in the case of a fixed frequency as well as in the case of a finite number of frequencies for Gaussian sequences and for sequences of independent random variables. The exact distribution is obtained in the case of a fixed frequence for one-dimensional GAUSsian sequences. Asymptotic expansions, respectively, the rate of convergence to the asymptotic distribution are given in the case mentioned above     

L Ranked Set Sampling: A Generalization Procedure for Robust Visual Sampling

In this article, a robust ranked set sampling (LRSS) scheme for estimating population mean is introduced. The proposed method is a generalization for many types of ranked set sampling that introduced in the literature for estimating the population mean. It is shown that the LRSS method gives unbiased estimator for the population mean with minimum variance providing that the underlying distribution is symmetric. However, for skewed distributions a weighted mean is given, where the optimal weights is computed by using Shannon's entropy. The performance of the population mean estimator is discussed along with its properties. Monte Carlo comparisons for detecting outliers are made with the traditional simple random sample and the ranked set sampling for some distributions. The results indicate that the LRSS estimator is superior alternative to the existing methods.     

Fast and rigorous: Configurational determinants of strategic decision-making balance

A longstanding debate in the strategic decision-making literature has focused on whether top management teams (TMTs) can effectively balance speed and comprehensiveness when making important decisions. In our research, we build on early insights and pivot from considering whether TMTs can engage indecision-making that balances these tensions to focus instead on when certain types of TMTs are able to achieve such balance. We employ a novel configurational analytical approach and a theoretical framework built from role theory to examine the CEO-TMT interface in a new way. In so doing, we are able to identify specific CEO-TMT constellations that support decision-making that is both fast and rigorous. Using a unique primary dataset and an abductive, configurational approach grounded in fuzzy set qualitative comparative analysis (fsQCA), we identify six specific leader-team configurations that each facilitate decision processes characterized by rigorous intra-team debate, meaningful reconciliation of divergent ideas, and fast decision speed (which we describe as strategic decision-making balance). The range of CEO-TMT configurations that emerge from our analyses contribute new theory and findings for the strategic decision-making and interface literatures more broadly, as well as the specific research streams on executive gender, humility, and TMT structure.