首页 | 本学科首页   官方微博 | 高级检索  
     检索      


Characterization of the multivariate Gauss-Markoff model with singular covariance matrix and missing values
Authors:Wiktor Oktaba
Institution:(1) Institute of Applied Mathematics, Department of Mathematical Statistics, Agricultural University, Akademicka 13, 20-934 Lublin, Poland
Abstract:The aim of this paper is to characterize the Multivariate Gauss-Markoff model (MGM) as in (2.1) with singular covariance matrix and missing values. MGMDP2 model and completed MGMDP2Q model are obtained by three transformations D, P and Q (cf. (3.21)) of MGM. The unified theory of estimation (Rao, 1973) which is of interest with respect to MGM has been used.The characterization is reached by estimation of parameters: scalar sgr2 and linear combination 
$$\lambda '\bar B\left( {\bar B = vecB} \right)$$
as in (4.8), (4.6), (4.7) as well as by the model of the form (5.1) (cf. Th. 5.1). Moreover, testing linear hypothesis in the available model MGMDP2 by test function F as in (6.3) and (6.4) is considered.It is known (Oktaba 1992) that ten quantities in models MGMDP2, and MGMDP2Q are identical (invariant). They permit to say that formulas for estimation and testing in both models are identical (Oktaba et al., 1988, Baksalary and Kala, 1981, Drygas, 1983).An algorithm and the UMGMBO program for calculations concerning estimation and testing in MGM have been presented by Oktaba and Osypiuk (1993).
Keywords:multivariate Gauss-Markoff model  missing value  developed model  available model  completed model  elementary transformation  BLUE  estimation  testing  consistency  invariant
本文献已被 SpringerLink 等数据库收录!
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号