共查询到20条相似文献,搜索用时 105 毫秒
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《数学的实践与认识》2020,(1)
在广义估计方程框架下,发展了一类灵活的回归模型来参数化协方差结构.通过合并广泛使用的修正的Cholesky分解和滑动平均Cholesky分解,得到自回归滑动平均Cholesky分解.该分解能够参数化更一般的协方差结构,且其输入具有清晰的统计解释.对这些输入建立回归模型,并利用拟Fisher迭代算法估计回归系数.均值和协方差模型中的参数估计皆具有相合性和渐近正态性.最后通过模拟研究考察了所提方法的有限样本表现. 相似文献
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线性混合模型中方差分量的广义推断 总被引:1,自引:0,他引:1
本文考虑了线性混合模型中方差分量的假设检验和区间估计问题.基于广义P-值和广义置信区间的概念,构造了对应于随机效应的单个方差分量的精确检验和置信区间.所构造的广义p-值和广义置信区间是最小充分统计量的函数.对于两个独立线性混合模型中对应于随机效应的方差分量的比较,建立了精确检验和置信区间.进-步,研究了所给检验和置信区间的统计性质,给出了这些检验方法与文献中已有方法的功效比较的模拟结果.模拟结果表明,新检验在功效方面有显著的改进.最后,通过-个实例来演示本文方怯. 相似文献
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本文提出一种针对纵向数据回归模型下的均值和协方差矩阵同时进行的有效稳健估计.基于对协方差矩阵的Cholesky分解和对模型的改写,我们提出一个加权最小二乘估计,其中权重是通过广义经验似然方法估计出来的.所提估计的有效性得益于经验似然方法的优势,稳健性则是通过限制残差平方和的上界来达到.模拟研究表明,和已有的针对纵向数据的稳健估计相比,所提估计具有更高的效率和可比的稳健性.最后,我们把所提估计方法用来分析一组实际数据. 相似文献
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在panel模型中,如果方差分量已知,对回归系数的检验,存在一致最优功效检验.但往往方差分量未知,这时采用的方法就是用它们的估计代替它们.不同的方差分量的估计,就得到不同的检验统计量.这些检验统计量的分布都是未知的,在小样本情况下,很难控制它们的检验水平.本文采用广义p值的方法,给出了一种精确的检验.模拟结果显示,这种检验能很好的控制检验水平,并且有更高的检验功效.同时,本文利用广义置信域的方法给出了回归系数的广义置信球. 相似文献
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针对偏正态非平衡面板单因素随机效应模型,文章研究了回归系数和方差分量函数的假设检验和区间估计问题.首先,基于矩阵分解技术,给出回归系数的精确检验方法.其次,利用Bootstrap方法和广义方法,构造单个方差分量、方差分量之和的检验统计量和置信区间.再次,建立方差分量之比的精确检验和近似检验.文章证明了所给检验方法和置信区间的变换不变性等理论性质.Monte Carlo结果表明,对于所设参数和样本量,文章所给方法在犯第一类错误的概率和功效意义下,具有统计优良性.最后,将上述方法应用于汽油消耗量的案例分析. 相似文献
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We develop methods to compare multiple multivariate normally distributed samples which may be correlated. The methods are new in the context that no assumption is made about the correlations among the samples. Three types of null hypotheses are considered: equality of mean vectors, homogeneity of covariance matrices, and equality of both mean vectors and covariance matrices. We demonstrate that the likelihood ratio test statistics have finite-sample distributions that are functions of two independent Wishart variables and dependent on the covariance matrix of the combined multiple populations. Asymptotic calculations show that the likelihood ratio test statistics converge in distribution to central Chi-squared distributions under the null hypotheses regardless of how the populations are correlated. Following these theoretical findings, we propose a resampling procedure for the implementation of the likelihood ratio tests in which no restrictive assumption is imposed on the structures of the covariance matrices. The empirical size and power of the test procedure are investigated for various sample sizes via simulations. Two examples are provided for illustration. The results show good performance of the methods in terms of test validity and power. 相似文献
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We compute the asymptotic distribution of the sample covariance matrix for independent and identically distributed random vectors with regularly varying tails. If the tails of the random vectors are sufficiently heavy so that the fourth moments do not exist, then the sample covariance matrix is asymptotically operator stable as a random element of the vector space of symmetric matrices. 相似文献
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Michael J. Daniels 《Journal of multivariate analysis》2006,97(5):1185-1207
We explore simultaneous modeling of several covariance matrices across groups using the spectral (eigenvalue) decomposition and modified Cholesky decomposition. We introduce several models for covariance matrices under different assumptions about the mean structure. We consider ‘dependence’ matrices, which tend to have many parameters, as constant across groups and/or parsimoniously modeled via a regression formulation. For ‘variances’, we consider both unrestricted across groups and more parsimoniously modeled via log-linear models. In all these models, we explore the propriety of the posterior when improper priors are used on the mean and ‘variance’ parameters (and in some cases, on components of the ‘dependence’ matrices). The models examined include several common Bayesian regression models, whose propriety has not been previously explored, as special cases. We propose a simple approach to weaken the assumption of constant dependence matrices in an automated fashion and describe how to compute Bayes factors to test the hypothesis of constant ‘dependence’ across groups. The models are applied to data from two longitudinal clinical studies. 相似文献
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In this paper, we focus on the tests for covariance matrices in panel data model with interactive fixed effects. For the problem of testing identity and sphericity of covariance matrices, we first propose test statistics based on the estimators of the trace of covariance matrices. Under both the null hypothesis and the alternatives, we establish the asymptotic distributions of the proposed test statistics under some regularity conditions, and we further show that the proposed tests are distribution free. Subsequently simulation studies suggest that the proposed tests perform well under the high dimensional panel data. 相似文献
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??In this paper, we focus on the tests for covariance matrices in panel data model with interactive fixed effects. For the problem of testing identity and sphericity of covariance matrices, we first propose test statistics based on the estimators of the trace of covariance matrices. Under both the null hypothesis and the alternatives, we establish the asymptotic distributions of the proposed test statistics under some regularity conditions, and we further show that the proposed tests are distribution free. Subsequently simulation studies suggest that the proposed tests perform well under the high dimensional panel data. 相似文献
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Jianqi Yu K. Krishnamoorthy Maruthy K. Pannala 《Journal of multivariate analysis》2006,97(10):2162-2176
Inferential procedures for the difference between two multivariate normal mean vectors based on incomplete data matrices with different monotone patterns are developed. Assuming that the population covariance matrices are equal, a pivotal quantity, similar to the Hotelling T2 statistic, is proposed, and its approximate distribution is derived. Hypothesis testing and confidence estimation of the difference between the mean vectors based on the approximate distribution are outlined. The validity of the approximation is investigated using Monte Carlo simulation. Monte Carlo studies indicate that the approximate method is very satisfactory even for small samples. A multiple comparison procedure is outlined and the proposed methods are illustrated using an example. 相似文献
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序约束下多元正态均值的检验问题 总被引:1,自引:0,他引:1
设有k组均值有简单半序约束,协方差阵未知的p维正态分布.Sasabuchi等在2003年研究了均值是否相等的检验问题.考虑到似然比检验统计量的临界点难以获得,以致于它不容易实施,Sasabuchi提出了一个检验方法.称为Sasabuchi检验.Sasabuchi检验的一个不足之处在于,它并不优于经典的MANOVA检验.作者提出了一个新的检验方法,它比Sasabuchi检验有一致优的势,而且形式更为简单.通过模拟发现这个检验方法还优势于MANOVA.最后导出了这个检验统计量的渐近零分布. 相似文献
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Modern random matrix theory indicates that when the population size p is not negligible with respect to the sample size n, the sample covariance matrices demonstrate significant deviations from the population covariance matrices. In order to recover the characteristics of the population covariance matrices from the observed sample covariance matrices, several recent solutions are proposed when the order of the underlying population spectral distribution is known. In this paper, we deal with the underlying order selection problem and propose a solution based on the cross-validation principle. We prove the consistency of the proposed procedure. 相似文献
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For several decades, much attention has been paid to the two-sample Behrens-Fisher (BF) problem which tests the equality of
the means or mean vectors of two normal populations with unequal variance/covariance structures. Little work, however, has
been done for the k-sample BF problem for high dimensional data which tests the equality of the mean vectors of several high-dimensional normal
populations with unequal covariance structures. In this paper we study this challenging problem via extending the famous Scheffe’s
transformation method, which reduces the k-sample BF problem to a one-sample problem. The induced one-sample problem can be easily tested by the classical Hotelling’s
T
2 test when the size of the resulting sample is very large relative to its dimensionality. For high dimensional data, however,
the dimensionality of the resulting sample is often very large, and even much larger than its sample size, which makes the
classical Hotelling’s T
2 test not powerful or not even well defined. To overcome this difficulty, we propose and study an L
2-norm based test. The asymptotic powers of the proposed L
2-norm based test and Hotelling’s T
2 test are derived and theoretically compared. Methods for implementing the L
2-norm based test are described. Simulation studies are conducted to compare the L
2-norm based test and Hotelling’s T
2 test when the latter can be well defined, and to compare the proposed implementation methods for the L
2-norm based test otherwise. The methodologies are motivated and illustrated by a real data example.
The work was supported by the National University of Singapore Academic Research Grant (Grant No. R-155-000-085-112) 相似文献
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On the k-sample Behrens-Fisher problem for high-dimensional data 总被引:1,自引:0,他引:1
For several decades,much attention has been paid to the two-sample Behrens-Fisher(BF) problem which tests the equality of the means or mean vectors of two normal populations with unequal variance/covariance structures.Little work,however,has been done for the k-sample BF problem for high dimensional data which tests the equality of the mean vectors of several high-dimensional normal populations with unequal covariance structures.In this paper we study this challenging problem via extending the famous Scheff... 相似文献