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Comparison of MINQUE and LMVQUIE by simulation. (English) Zbl 1080.62529

Summary: An analytical expression for the density function of the minimum norm quadratic unbiased estimator (MINQUE) or of the locally minimum variance quadratic unbiased invariant estimator (LMVQUIE) of the variance components in a mixed linear model is unknown even if the observation vector is normally distributed. In comparison with the LMVQUIE, which requires the knowledge of the third and fourth moments of the observation vector, the MINQUE, which does not require it, seems to be more suitable for practical purposes. Density functions induced by MINQUE and LMVQUIE from several basic distributions and differences between them are analyzed by simulation. The theoretical variances of the LMVQUIE and the MINQUE are compared as well.

MSC:

62J10 Analysis of variance and covariance (ANOVA)
62F10 Point estimation
65C60 Computational problems in statistics (MSC2010)
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References:

[1] Cramér H.: Mathematical Methods of Statistics. Princeton University Press, Princeton, 1946. · Zbl 0063.01014
[2] Hsu P. L.: On the best unbiased quadratic estimate of the variance. In.: (K. L. Chung Poa-Lu Hsu collected papers. Springer, Berlin 1983, 55-68.
[3] Kleffe J.: Simultaneous estimation of expectation and covariance matrix in linear models. AdW de DDR Zentralinstitut für Mathematik und Mechanik (preprint), Berlin, 1977. · Zbl 0415.62026 · doi:10.1080/02331887808801444
[4] Kubáček L.: Reliability of calculation in the linear estimation and some problems of the analysis of a multistage regression experiment. In.: (T. Havránek, Z. Šidák, M. Novák Compstat 1984, Physica Verlag, Vienna, 1984, 214-224.
[5] Kubáček L.: Locally best quadratic estimators. Mathematica Slovaca 35 (1985), 393-408. · Zbl 0597.62050
[6] Kubáček L.: Multistage regression model. Aplikace matematiky 31 (1986), 89-96. · Zbl 0595.62062
[7] Kubáček L.: Foundations of Estimation Theory. Elsevier, Amsterdam-Oxford-New York-Tokyo, 1988.
[8] Rao C. R.: Linear Statistical Inference and Its Applications. J. Wiley, New York, 1965. · Zbl 0137.36203
[9] Rao C. R., Mitra S. K.: Generalized Inverse of Matrices and Its Applications. J. Wiley, New York, 1971. · Zbl 0236.15004
[10] Rao C. R., Kleffe J.: Estimation of variance components. In.: (P. R. Krishnaiah Handbook of Statistics, Vol I, North-Holland, New York, 1980, 1-40. · Zbl 0476.62058
[11] Volaufová J.: Estimation of parameters of mean and variance in two-stage linear models. Aplikace matematiky 32 (1987), 1-8. · Zbl 0616.62091
[12] Volaufová J.: Note on estimation of parameters of mean and variance in n-stage linear models. Aplikace matematiky 33 (1988), 41-48. · Zbl 0635.62067
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