Characterization of Admissible Linear Estimators in Multivariate Linear Model with Respect to Inequality Constraints under Matrix Loss Function

In this article, we study the characterization of admissible linear estimators in a multivariate linear model with inequality constraint, under a matrix loss function. In the homogeneous class, we present several equivalent, necessary and sufficient conditions for a linear estimator of estimable functions to be admissible. In the inhomogeneous class, we find that the necessary and sufficient conditions depend on the rank of the matrix in the constraint. When the rank is greater than one, the necessary and sufficient conditions are obtained. When the rank is equal to one, we have necessary conditions and sufficient conditions separately. We also obtain the necessary and sufficient conditions for a linear estimator of inestimable function to be admissible in both classes.     

中国金融资金流量矩阵表延长模型研究

金融资金流量矩阵表具有重要应用价值,然而我国资金流量表只采用账户表式,而且数据滞后严重,使其应用价值难以实现。本文在对资金流量矩阵表表式结构、账户分类和平衡关系进行深入理解的基础上,将计量经济模型中的多元回归模型、时间序列模型、状态空间模型及RAS模型有效地组合在一起,设计了一套延长金融资金流量矩阵表的组合模型,然后应用该模型将我国金融资金流量矩阵表从2009年延长至2012年。经后验法检验,数据质量达到了一个较为理想的状态。这套模型可以作为官方统计机构或民间研究机构延长资金流量表数据的通用方法使用。     

Inference in affine shape theory under elliptical models

This paper studies the elliptical statistical affine shape theory under certain particular conditions on the evenness or oddness of the number of landmarks. In such a case, the related distributions are polynomials, and the inference is easily performed; as an example, a landmark data is studied, and the performance of the polynomial density versus the usual series density is compared.     

Moments and quadratic forms of matrix variate skew normal distributions

ABSTRACT

In 2007, Domínguez-Molina et al. obtained the moment generating function (mgf) of the matrix variate closed skew normal distribution. In this paper, we use their mgf to obtain the first two moments and some additional properties of quadratic forms for the matrix variate skew normal distributions. The quadratic forms are particularly interesting because they are essentially correlation tests that introduce a new type of orthogonality condition.     

More on the two-parameter estimation in the restricted regression

ABSTRACT

In this paper, we introduce a new restricted two-parameter (RTP) estimator for the vector of parameters in a linear model when additional linear restrictions on the parameter vector are assumed to hold. We show that our new biased estimator is superior in the matrix mean square error criterion to the restricted ridge estimator proposed by Groß (2003 Groß, J. (2003). Restricted ridge estimation. Stat. Probab. Lett. 65:57–64.[Crossref], [Web of Science ®] , [Google Scholar]), restricted Liu estimator introduced by Kaçiranlar et al. (1999 Kaçiranlar, S., Sakall?oglus, S., Akdeniz, F., Styan, G.P.H., Werner, H.J. (1999). A new biased estimator in linear regression and a detailed analysis of the widely-analysed dataset on Portland cement. Sankhya Ser. B., Ind. J. Stat. 61:443–459. [Google Scholar]), and RTP estimator introduced by Özkale and Kaçiranlar (2007 Özkale, M., Kaçiranlar, S. (2007). The restricted and unrestricted two-parameter estimators. Commun. Stat. Theory Methods 36:2707–2725.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). A numerical example and a Monte Carlo simulation have been analyzed to illustrate some of the theoretical results.     

Number of appearances of events in random sequences: A new approach to non-overlapping runs

ABSTRACT

Distributions of non-overlapping runs in multistate systems are derived using a new generating function (GF) approach, which has been applied previously mainly to exact length runs. By utilizing this method, univariate and multivariate joint distributions of non-overlapping runs are derived in a unified way. The GF approach also leads naturally to the asymptotic Gaussian distributions, with the mean, variance, and covariance linear in the size of the system.     

Bounds on the regression coefficients when a covariate is categorized

This paper considers the problem of a linear regression model in which a continuous covariate is categorized. In such a case one can obtain bounds on the OLS-estimate which would be calculated if the complete information were available. These bounds give an indication of the information loss due to grouping and show what can be inferred from the data without additional assumptions.     

Matrix mean squared error comparisons of some biased estimators with two biasing parameters

To deal with multicollinearity problem, the biased estimators with two biasing parameters have recently attracted much research interest. The aim of this article is to compare one of the last proposals given by Yang and Chang (2010 Yang, H., and X. Chang. 2010. A new two-parameter estimator in linear regression. Communications in Statistics: Theory and Methods 39 (6):923–34.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) with Liu-type estimator (Liu 2003 Liu, K. 2003. Using Liu-type estimator to combat collinearity. Communications in Statistics: Theory and Methods 32 (5):1009–20.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) and k ? d class estimator (Sakallioglu and Kaciranlar 2008 Sakallioglu, S., and S. Kaciranlar. 2008. A new biased estimator based on ridge estimation. Statistical Papers 49:669–89.[Crossref], [Web of Science ®] , [Google Scholar]) under the matrix mean squared error criterion. As well as giving these comparisons theoretically, we support the results with the extended simulation studies and real data example, which show the advantages of the proposal given by Yang and Chang (2010 Yang, H., and X. Chang. 2010. A new two-parameter estimator in linear regression. Communications in Statistics: Theory and Methods 39 (6):923–34.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) over the other proposals with increasing multicollinearity level.     

Sharpley-Snow定理证明的注记

本文给出了对策论中著名的Sharpley-Snow定理必要性的另一证明,明确了其中非奇异矩阵B的取法,且证明方法不同于单纯形证法。     

模糊偏序关系及其在消费者广告偏好方面的运用

本文提出建立模糊偏序关系矩阵的可行途径,以大学生广告媒体偏好实验为例,论证了采用本文所建立的模糊偏序关系矩阵进行排序的方法是研究消费者广告偏好的一种较佳的方法。同时讨论了模糊偏序法的利与弊。