Least-squares variance component estimation |
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Authors: | P J G Teunissen A R Amiri-Simkooei |
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Institution: | (1) Delft Institute of Earth Observation and Space systems (DEOS), Faculty of Aerospace Engineering, Delft University of Technology, Kluyverweg 1, 2629 HS Delft, The Netherlands;(2) Department of Surveying Engineering, Faculty of Engineering, The University of Isfahan, 81744, Isfahan, Iran |
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Abstract: | Least-squares variance component estimation (LS-VCE) is a simple, flexible and attractive method for the estimation of unknown
variance and covariance components. LS-VCE is simple because it is based on the well-known principle of LS; it is flexible
because it works with a user-defined weight matrix; and it is attractive because it allows one to directly apply the existing
body of knowledge of LS theory. In this contribution, we present the LS-VCE method for different scenarios and explore its
various properties. The method is described for three classes of weight matrices: a general weight matrix, a weight matrix
from the unit weight matrix class; and a weight matrix derived from the class of elliptically contoured distributions. We
also compare the LS-VCE method with some of the existing VCE methods. Some of them are shown to be special cases of LS-VCE.
We also show how the existing body of knowledge of LS theory can be used to one’s advantage for studying various aspects of
VCE, such as the precision and estimability of VCE, the use of a-priori variance component information, and the problem of
nonlinear VCE. Finally, we show how the mean and the variance of the fixed effect estimator of the linear model are affected
by the results of LS-VCE. Various examples are given to illustrate the theory. |
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Keywords: | Least-squares variance component estimation (LS-VCE) Elliptically contoured distribution Best linear unbiased estimator (BLUE) Best invariant quadratic unbiased estimator (BIQUE) Minimum norm quadratic unbiased estimator (MINQUE) Restricted maximum likelihood estimator (REML) |
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