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university of tampere: sis/luo-coms: research: cis - the tampere research center for information and systems: research groups: statistics group:
Faculties of Natural and Communication SciencesUniversity of TampereFaculties of Natural and Communication Sciences
CIS - The Tampere Research Center for Information and Systems

Research

Linear Statistical Models and Related Matrix Algebra

The research on linear statistical models and related matrix algebra deals with topics related to linear estimation and prediction in the general linear model. The main contributions concern the concepts of the best linear unbiased estimation, BLUE, of the best linear unbiased prediction, BLUP, linear sufficiency, linear prediction sufficiency, the ordinary least squares estimator, OLSE, and the Watson efficiency.

Some new characterizations for linear sufficiency and linear completeness in a case of estimation of the parametric function are given, and also a predictive approach for obtaining the BLUE of the estimable parametric functions is considered. In the context of predicting the value of new observation under the general linear model, a new concept, linear prediction sufficiency, is introduced.

The equality of OLSE and BLUE of the given estimable parametric function is considered and properties of the Watson efficiency are investigated particularly under the partitioned linear model. Similarly, the difference between the BLUEs under two linear models (having different covariance matrices) is studied. Considering two mixed linear models, M1 and M2, say, which have different covariance matrices, some new necessary and sufficient conditions are given, without making any rank assumptions, that every representation of the BLUP of the random effect under the model M1 continues to be BLUP under the model M2. These considerations are generalized to two linear models with new unobserved future observations.

Also,  mixed linear models, possibly with singular covariance matrices, can be supplemented by a particular fixed effects model with appropriate stochastic restrictions. Then all representations of the BLUE and BLUP can be obtained through the augmented model including stochastic restrictions.

A good idea about the research interest in linear statistical models and related matrix algebra can be obtained from a recent book Puntanen, Simo; Styan, George P. H. & Isotalo, Jarkko (2011). Matrix Tricks for Linear Statistical Models: Our Personal Top Twenty. Springer. DOI: http://dx.doi.org/10.1007/978-3-642-10473-2.

 
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Last update: 13.3.2012 22.33 Muokkaa

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