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文章按照统一的思路系统地定义了总体或样本的协方差(矩阵)和相关系数(矩阵).同时也给出了这些概念的一些性质. 相似文献
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高维协方差矩阵的估计问题现已成为大数据统计分析中的基本问题,传统方法要求数据满足正态分布假定且未考虑异常值影响,当前已无法满足应用需要,更加稳健的估计方法亟待被提出。针对高维协方差矩阵,一种稳健的基于子样本分组的均值-中位数估计方法被提出且简单易行,然而此方法估计的矩阵并不具备正定稀疏特性。基于此问题,本文引进一种中心正则化算法,弥补了原始方法的缺陷,通过在求解过程中对估计矩阵的非对角元素施加L1范数惩罚,使估计的矩阵具备正定稀疏的特性,显著提高了其应用价值。在数值模拟中,本文所提出的中心正则稳健估计有着更高的估计精度,同时更加贴近真实设定矩阵的稀疏结构。在后续的投资组合实证分析中,与传统样本协方差矩阵估计方法、均值-中位数估计方法和RA-LASSO方法相比,基于中心正则稳健估计构造的最小方差投资组合收益率有着更低的波动表现。 相似文献
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Hamilton以及Pelletier提出了基于机制转换的动态相关系数矩阵模型,适合于具有方差时变特性的金融时间序列的应用.文章利用随机矩阵理论对该模型中的相关系数矩阵作了改进,去掉其中的噪声,留下真实的信息,并用改进后的模型对中国股市中的股票进行优化组合研究,取得了较好的结果.从而为动态投资组合优化提供了一个强有力的工具. 相似文献
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0引言模糊聚类中的最大树法是直接对模糊相似关系矩阵进行分析,该方法尤其适用于待分类样本数量多的情况。目前相关文献大致有欧氏距离、切比雪夫距离、相关系数等十三种确定模糊相似关系矩阵元素的方法,但最常用的方法是绝对值减数法:γij=1i=j1-cmk=1∑|χik-χjk|i≠(1)其 相似文献
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对随机效应空间滞后单指数面板模型,本文构建了该模型的截面极大似然估计方法,从理论证明和数值模拟两方面分别考察了其估计量的大样本性质和小样本表现。研究结果表明:(1)在大样本条件下,估计量均具有一致性,并且参数估计量具有渐近正态性。(2)在小样本条件下,各估计量依然具有良好的表现,其精度随着样本容量的增加而提高;空间权重矩阵结构的复杂性对空间相关系数的估计量影响较大,但对其他估计量的影响较小。 相似文献
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对灰色层次分析法中基于灰色判断矩阵的一致性和排序问题进行了研究。提出了灰色判断矩阵的弱一致性和乘性完全一致性的条件,然后讨论了在单一准则下基于灰色判断矩阵的方案集排序问题。方法一将灰色判断矩阵转化为白化矩阵,通过研究白化矩阵的性质来对方案集进行排序,方法二是将其转化为区间灰数互补判断矩阵,再利用OWA算子对方案集集结进而进行排序。最后通过算例说明了该方法的有效性。 相似文献
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社会核算矩阵就是以矩阵的形式反映的国民核算体系.它是目前组织国民经济核算数据最常用的工具之一.与其他方法相比,它具有简明、体系性强、可向细化发展等特点.文章以联合国编著的1993年国民经济核算体系(1993sNA)为蓝本采用一套国民经济模拟数据解读了社会核算矩阵的主要功能.正确解读社会核算矩阵,可以对国民经济运行过程的数量描述把握得更加清晰和准确. 相似文献
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《Journal of Statistical Computation and Simulation》2012,82(14):2707-2713
ABSTRACTStress testing correlation matrix is a challenging exercise for portfolio risk management. Most existing methods directly modify the estimated correlation matrix to satisfy stress conditions while maintaining positive semidefiniteness. The focus lies on technical optimization issues but the resultant stressed correlation matrices usually lack statistical interpretations. In this article, we suggest a novel approach using Empirical Likelihood method to modify the probability weights of sample observations to construct a stressed correlation matrix. The resultant correlations correspond to a stress scenario that is nearest to the observed scenario in a Kullback–Leibler divergence sense. Besides providing a clearer statistical interpretation, the proposed method is non-parametric in distribution, simple in computation and free from subjective tunings. We illustrate the method through an application to a portfolio of international assets. 相似文献
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Alphonse K. A. Amey 《统计学通讯:模拟与计算》2013,42(4):1443-1457
The density of the multiple correlation coefficient is derived by direct integration when the sample covariance matrix has a linear non-central distribution. Using the density, we deduce the null and non-null distribution of the multiple correlation coefficient when sampling from a mixture of two multivariate normal populations with the same covariance matrix. We also compute actual significance levels of the test of the hypothesis Ho : ρ1·2…p = 0 versus Ha:ρ1·2…p > 0, given the mixture model. 相似文献
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Daisuke Nagakura 《统计学通讯:理论与方法》2018,47(13):3252-3268
We introduce a matrix operator, which we call “vecd” operator. This operator stacks up “diagonals” of a symmetric matrix. This operator is more convenient for some statistical analyses than the commonly used “vech” operator. We show an explicit relationship between the vecd and vech operators. Using this relationship, various properties of the vecd operator are derived. As applications of the vecd operator, we derive concise and explicit expressions of the Wald and score tests for equal variances of a multivariate normal distribution and for the diagonality of variance coefficient matrices in a multivariate generalized autoregressive conditional heteroscedastic (GARCH) model, respectively. 相似文献
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The Gaussian rank correlation equals the usual correlation coefficient computed from the normal scores of the data. Although
its influence function is unbounded, it still has attractive robustness properties. In particular, its breakdown point is
above 12%. Moreover, the estimator is consistent and asymptotically efficient at the normal distribution. The correlation
matrix obtained from pairwise Gaussian rank correlations is always positive semidefinite, and very easy to compute, also in
high dimensions. We compare the properties of the Gaussian rank correlation with the popular Kendall and Spearman correlation
measures. A simulation study confirms the good efficiency and robustness properties of the Gaussian rank correlation. In the
empirical application, we show how it can be used for multivariate outlier detection based on robust principal component analysis. 相似文献
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Stephen W. Looney 《统计学通讯:模拟与计算》2013,42(2):531-543
It is often of interest to test the hypothesis that all off-diagonal elements of the correlation matrix of a multivariate normal distribution are equal. If the hypothesis of equal correlation can be accepted, it then may be of interest to estimate the common correlation coefficient. In this paper, four estimators of the common correlation are compared in terms of bias, variance, mean squared error, adequacy of the normal approximation, and ease of calculation. The average sample correlation is seen to be comparable to the other estimators and is recommended here since it is the easiest to calculate. The estimators are compared using simulation. 相似文献
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《Journal of Statistical Computation and Simulation》2012,82(11):1065-1076
Sampling the correlation matrix (R) plays an important role in statistical inference for correlated models. There are two main constraints on a correlation matrix: positive definiteness and fixed diagonal elements. These constraints make sampling R difficult. In this paper, an efficient generalized parameter expanded re-parametrization and Metropolis-Hastings (GPX-RPMH) algorithm for sampling a correlation matrix is proposed. Drawing all components of R simultaneously from its full conditional distribution is realized by first drawing a covariance matrix from the derived parameter expanded candidate density (PXCD), and then translating it back to a correlation matrix and accepting it according to a Metropolis-Hastings (M-H) acceptance rate. The mixing rate in the M-H step can be adjusted through a class of tuning parameters embedded in the generalized candidate prior (GCP), which is chosen for R to derive the PXCD. This algorithm is illustrated using multivariate regression (MVR) models and a simulation study shows that the performance of the GPX-RPMH algorithm is more efficient than that of other methods. 相似文献
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Andrea A. Prudente 《统计学通讯:理论与方法》2013,42(20):3739-3755
For the first time, a new class of generalized Weibull linear models is introduced to be competitive to the well-known generalized (gamma and inverse Gaussian) linear models which are adequate for the analysis of positive continuous data. The proposed models have a constant coefficient of variation for all observations similar to the gamma models and may be suitable for a wide range of practical applications in various fields such as biology, medicine, engineering, and economics, among others. We derive a joint iterative algorithm for estimating the mean and dispersion parameters. We obtain closed form expressions in matrix notation for the second-order biases of the maximum likelihood estimates of the model parameters and define bias corrected estimates. The corrected estimates are easily obtained as vectors of regression coefficients in suitable weighted linear regressions. The practical use of the new class of models is illustrated in one application to a lung cancer data set. 相似文献
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Anders Løland Ragnar Bang Huseby Nils Lid Hjort Arnoldo Frigessi 《Scandinavian Journal of Statistics》2013,40(4):807-824
Suppose estimates are available for correlations between pairs of variables but that the matrix of correlation estimates is not positive definite. In various applications, having a valid correlation matrix is important in connection with follow‐up analyses that might, for example, involve sampling from a valid distribution. We present new methods for adjusting the initial estimates to form a proper, that is, nonnegative definite, correlation matrix. These are based on constructing certain pseudo‐likelihood functions, formed by multiplying together exact or approximate likelihood contributions associated with the individual correlations. Such pseudo‐likelihoods may then be maximized over the range of proper correlation matrices. They may also be utilized to form pseudo‐posterior distributions for the unknown correlation matrix, by factoring in relevant prior information for the separate correlations. We illustrate our methods on two examples from a financial time series and genomic pathway analysis. 相似文献
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Srivastava (1980) showed that Grubbs's test for detecting a univariate outlier is robust against the effect of intraclass correlation structure. Young, Pavur, and Marco (1989) extended this result by proving that both the significance level and the power of Grubbs's test remain unchanged within a wider family of dispersion matrices, introduced by Baldessari (1966) in a different context. In this note, we derive a complete solution of the problem by establishing that the characteristics of Grubbs's test are invariant with respect to a given dispersion matrix if and only if it has Baldessari's structure. 相似文献