Robust methods of estimation of regression coefficients 1

Recently, cumulative residual entropy (CRE) has been found to be a new measure of information that parallels Shannon's entropy (see Rao et al. [Cumulative residual entropy: A new measure of information, IEEE Trans. Inform. Theory. 50(6) (2004), pp. 1220–1228] and Asadi and Zohrevand [On the dynamic cumulative residual entropy, J. Stat. Plann. Inference 137 (2007), pp. 1931–1941]). Motivated by this finding, in this paper, we introduce a generalized measure of it, namely cumulative residual Renyi's entropy, and study its properties. We also examine it in relation to some applied problems such as weighted and equilibrium models. Finally, we extend this measure into the bivariate set-up and prove certain characterizing relationships to identify different bivariate lifetime models.     

Maximum entropy sampling and optimal Bayesian experimental design

When Shannon entropy is used as a criterion in the optimal design of experiments, advantage can be taken of the classical identity representing the joint entropy of parameters and observations as the sum of the marginal entropy of the observations and the preposterior conditional entropy of the parameters. Following previous work in which this idea was used in spatial sampling, the method is applied to standard parameterized Bayesian optimal experimental design. Under suitable conditions, which include non-linear as well as linear regression models, it is shown in a few steps that maximizing the marginal entropy of the sample is equivalent to minimizing the preposterior entropy, the usual Bayesian criterion, thus avoiding the use of conditional distributions. It is shown using this marginal formulation that under normality assumptions every standard model which has a two-point prior distribution on the parameters gives an optimal design supported on a single point. Other results include a new asymptotic formula which applies as the error variance is large and bounds on support size.     

A new estimator of entropy

Vasicek (1976) proposed an estimator of entropy based on spacings. A new estimator of entropy is proposed. This new estimator is based on local linear regression. Comparisons between this new estimator and Vasicek's estimator are made. The mean square error (MSE) of the new estimator is consistently smaller than the MSE of Vasicek's estimator.     

Measures of dependence for the multivariate t distribution with applications to the stock market

Two measures of dependence for multivariate t and Cauchy random variables are developed based on Kullback–Leibler number. The mutual information number T(X) is obtained in a closed expression form, as well as its asymptotic distribution. A dependence coefficient ρ₁, is defined (based on the Kullback–Leibler number) with the properties of ρ₁=0 indicating independence and ρ₁=1indicating degeneracy. Two real life examples from the stock market are used to analyze the level of dependence and correlation among stocks.     

Estimation of signal to noise ratio using mahalanobis distance

In this paper, we propose some alternative estimatiors to that given by C. G. Khatri and C. R. Rao (1985), for estimating Signal to Noise ratio. Using Pitman Nearness, Condition for prefering one estimator over the other is estabilished. It is shown numerically that estimators corresponding to Entropy loss function are better more oftern than those corresponding to Squared Error loss.     

Confidence Intervals for Gini's Diversity Measure and Shannon's Entropy Using Adjusted Proportions

Abstract

Asymptotic confidence intervals are given for two functions of multinomial outcome probabilities: Gini's diversity measure and Shannon's entropy. “Adjusted” proportions are used in all asymptotic mean and variance formulas, along with a possible logarithmic transformation. Exact confidence coefficients are computed in some cases. Monte Carlo simulation is used in other cases to compare actual coverages to nominal ones. Some recommendations are made.     

算法隐含并行性的物理模型

利用物理学原理对算法的隐含并行性进行了分析,提出算法的不确定性和高熵态是隐含并行性出现的根源,但算法的隐含并行性会导致算法结果的不确定性。智能算法中先验知识确定程序的搜索方向,隐含并行性提供了对解空间的高速并行搜索,为研究和设计智能算法提供了理论基础。提高算法的先验信息量和隐含并行能力可以得到具备较高智能水平的算法。     

基于AHP法和熵权法的独立学院教师绩效考核

文章针对独立学院教师绩效考核过程中存在指标体系不健全、考核成绩计算过程中各项目权重分配不科学等问题,提出将基于层次分析法的主观赋权法与基于熵的客观赋权法相结合的主客观赋权法,以此提高权重分配的科学性与准确性;最后,选取某独立学院的教师进行实证分析.     

Interval censored and truncated data: Rate of convergence of NPMLE of the density

We consider survival data that are both interval censored and truncated. Under appropriate assumptions on the involved distributions, the censoring, truncation and survival, we prove the consistency of the NPMLE of the density of the survival, and give the rate of convergence. Finally, we give an example where the joint law of the censoring and truncation can be explicitly computed.     

基于熵值法的城市可持续发展评价模型

城市可持续发展应是一个城市经济发展、社会进步、环境支持三者保持高度和谐的过程。用熵值法能构造出经济发展、社会进步和环境支持指数三个复合指标,设计出评价城市可持续发展的可持续系数和协调系数。基于熵值法的城市可持续发展评价方法,合理地解决了评价中关于发展水平、速度和子系统协调性的关系,丰富了可持续发展评价问题的解决途径,实证研究的结果表明该评价方法是有效的。