Modified regression estimators using robust regression methods and covariance matrices in stratified random sampling

Abstract

This article proposes new regression-type estimators by considering Tukey-M, Hampel M, Huber MM, LTS, LMS and LAD robust methods and MCD and MVE robust covariance matrices in stratified sampling. Theoretically, we obtain the mean square error (MSE) for these estimators. We compare the efficiencies based on MSE equations, between the proposed estimators and the traditional combined and separate regression estimators. As a result of these comparisons, we observed that our proposed estimators give more efficient results than traditional approaches. And, these theoretical results are supported with the aid of numerical examples and simulation based on data sets that include outliers.     

Precise asymptotics on spectral statistics of random matrices

This paper focuses on the limiting properties of the spectral statistics of Wigner matrices and sample covariance matrices. Following the ideas of Gut and Spaˇtaru (2000a, b), Gut and Steinebach (2013) and Chow (1988) on precise asymptotics of i.i.d. random variables in the context of complete convergence and moment convergence, we will establish the corresponding results on the spectral statistics of random matrices.     

A note on the generalisation of cochran’s theorem

Khatri (1968) has extended Cochran’s theorem (1934) to matrices which are not necessarily symmetric. An alternative proof of the theorem is furnished here with some generalization with respect to one of Khatri’s conditions.     

自旋空间的对称面

本文提出了电子自旋空间的对称面概念，分析并讨论了电子自旋的本征态以及电子自旋角动量分量的平均值等问题。     

What's Wrong with Hazard‐Ranking Systems? An Expository Note

Two commonly recommended principles for allocating risk management resources to remediate uncertain hazards are: (1) select a subset to maximize risk-reduction benefits (e.g., maximize the von Neumann-Morgenstern expected utility of the selected risk-reducing activities), and (2) assign priorities to risk-reducing opportunities and then select activities from the top of the priority list down until no more can be afforded. When different activities create uncertain but correlated risk reductions, as is often the case in practice, then these principles are inconsistent: priority scoring and ranking fails to maximize risk-reduction benefits. Real-world risk priority scoring systems used in homeland security and terrorism risk assessment, environmental risk management, information system vulnerability rating, business risk matrices, and many other important applications do not exploit correlations among risk-reducing opportunities or optimally diversify risk-reducing investments. As a result, they generally make suboptimal risk management recommendations. Applying portfolio optimization methods instead of risk prioritization ranking, rating, or scoring methods can achieve greater risk-reduction value for resources spent.     

矩阵的存储及存储地址研究

探讨了一般矩阵、特殊矩阵和稀疏矩阵在内存中的存储以及如何根据矩阵的不同特点来确定它在存储时的元素个数和存储空间的大小及各个元素在内存中的存储地址。     

a bayesian analysis of the multivariate mixed-linear model

The Bayesian analysis of the multivariate mixed linear model is considered. The exact posterior distribution for the fixed effects matrix and the error covariance matrix are obtained. The exact posterior means and variances of the Bayesian estimators for the covariance matrices of random effects are also derived. These posterior moments are computed without constrained optimization and numerical integration. The calculations are feasible for arbitrary models. Reasonable approximations for the posterior distributions for the covariance matrices associated with the random effects are obtained also. Results are illustrated with a numerical example.     

The likelihood ratio test foe the homogeneity of the variances in a covariance matrix with block compound symmetry

For the problem of testing the homogeneity of the variances in a covariance matrix with a block compound symmetric structure, the likelihood ratio test is derived in this paper, A modification of the test that allows its distribution to be better approximated by the chi-square distribution is also considered, Formulae for calculating approximate sample size and power are derived, Small sample performances of these tests in the case of two dependent bivariate or trivariate normals are compared to each other and to the competing tests by simulating levels of significance and powers, and recommendation is made of the ones that have good performance, The recommended tests are then demonstrated in an illustrative example.     

两个正定矩阵乘积正定性的判别

文章对某些矩阵的乘积的正定性作一些探讨,在引用一定定理的基础上,给出其正定的一些判别。