Characterization of the multivariate Gauss-Markoff model with singular covariance matrix and missing values

Wiktor Oktaba

Applications of Mathematics (1998)

  • Volume: 43, Issue: 2, page 119-131
  • ISSN: 0862-7940

Abstract

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The aim of this paper is to characterize the Multivariate Gauss-Markoff model ( M G M ) as in () with singular covariance matrix and missing values. M G M D P 2 model and completed M G M D P 2 Q model are obtained by three transformations D , P and Q (cf. ()) of M G M . The unified theory of estimation (Rao, 1973) which is of interest with respect to M G M has been used. The characterization is reached by estimation of parameters: scalar σ 2 and linear combination λ ' B ¯ ( B ¯ = v e c B ) as in (), (), () as well as by the model of the form () (cf. Th. ). Moreover, testing linear hypothesis in the available model M G M D P 2 by test function F as in () and () is considered. It is known (Oktaba 1992) that ten quantities in models M G M D P 2 and M G M D P 2 Q 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 U M G M B O program for calculations concerning estimation and testing in M G M have been presented by Oktaba and Osypiuk (1993).

How to cite

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Oktaba, Wiktor. "Characterization of the multivariate Gauss-Markoff model with singular covariance matrix and missing values." Applications of Mathematics 43.2 (1998): 119-131. <http://eudml.org/doc/33002>.

@article{Oktaba1998,
abstract = {The aim of this paper is to characterize the Multivariate Gauss-Markoff model $(MGM)$ as in () with singular covariance matrix and missing values. $MGMDP2$ model and completed $MGMDP2Q$ model are obtained by three transformations $D$, $P$ and $Q$ (cf. ()) 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 $\sigma ^\{2\}$ and linear combination $\lambda ^\{\prime \}\bar\{B\}$ ( $\bar\{B\}=vecB)$ as in (), (), () as well as by the model of the form () (cf. Th. ). Moreover, testing linear hypothesis in the available model $MGMDP2$ by test function $F$ as in () and () 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).},
author = {Oktaba, Wiktor},
journal = {Applications of Mathematics},
keywords = {multivariate Gauss-Markoff model; missing value; developed model; available model; completed model; elementary transformation; BLUE; estimation; testing; consistency; invariant; multivariate Gauss-Markoff model; missing values; BLUE},
language = {eng},
number = {2},
pages = {119-131},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Characterization of the multivariate Gauss-Markoff model with singular covariance matrix and missing values},
url = {http://eudml.org/doc/33002},
volume = {43},
year = {1998},
}

TY - JOUR
AU - Oktaba, Wiktor
TI - Characterization of the multivariate Gauss-Markoff model with singular covariance matrix and missing values
JO - Applications of Mathematics
PY - 1998
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 43
IS - 2
SP - 119
EP - 131
AB - The aim of this paper is to characterize the Multivariate Gauss-Markoff model $(MGM)$ as in () with singular covariance matrix and missing values. $MGMDP2$ model and completed $MGMDP2Q$ model are obtained by three transformations $D$, $P$ and $Q$ (cf. ()) 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 $\sigma ^{2}$ and linear combination $\lambda ^{\prime }\bar{B}$ ( $\bar{B}=vecB)$ as in (), (), () as well as by the model of the form () (cf. Th. ). Moreover, testing linear hypothesis in the available model $MGMDP2$ by test function $F$ as in () and () 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).
LA - eng
KW - multivariate Gauss-Markoff model; missing value; developed model; available model; completed model; elementary transformation; BLUE; estimation; testing; consistency; invariant; multivariate Gauss-Markoff model; missing values; BLUE
UR - http://eudml.org/doc/33002
ER -

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