Geodesic
Extensions of the Frisch-Waugh-Lovell Theorem
Discussiones Mathematicae. Probability and Statistics, Tome 25 (2005) no. 1, pp. 39-49.

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In this paper we introduce extensions of the so-called Frisch-Waugh-Lovell Theorem. This is done by employing the close relationship between the concept of linear sufficiency and the appropriate reduction of linear models. Some specific reduced models which demonstrate alternatives to the Frisch-Waugh-Lovell procedure are discussed.
Keywords: best linear unbiased estimation, Frisch-Waugh-Lovell Theorem, linear sufficiency, orthogonal projector, partitioned linear model, reduced linear model 
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Groß, Jürgen; Puntanen, Simo. Extensions of the Frisch-Waugh-Lovell Theorem. Discussiones Mathematicae. Probability and Statistics, Tome 25 (2005) no. 1, pp. 39-49. http://geodesic.mathdoc.fr/item/DMPS_2005_25_1_a1/

[1] J.K. Baksalary and R. Kala, Linear sufficiency with respect to a given vector of parametric functions, Journal of Statistical Planning and Inference 14 (1986), 331-338.

[2] P. Bhimasankaram and R. Saha Ray, On a partitioned linear model and some associated reduced models, Linear Algebra and Its Applications 264 (1997), 329-339.

[3] P. Bhimasankaram and D. Sengupta, The linear zero functions approach to linear models, Sankhyā, Ser. B 58 (1996), 338-351.

[4] P. Bhimasankaram, K.R. Shah and R. Saha Ray, On a singular partitioned linear model and some associated reduced models, Journal of Combinatorics, Information System Sciences 23 (1998), 415-421.

[5] R. Davidson and J.G. MacKinnon, Estimation and Inference in Econometrics, Oxford University Press 1993.

[6] H. Drygas, Linear sufficiency and some applications in multilinear estimation, Journal of Multivariate Analysis 16 (1985), 71-84.

[7] A. Feuerverger and D.A.S. Fraser, Categorial information and the singular linear model, Canadian Journal of Statistics 8 (1980), 41-45.

[8] R. Frisch and F.V. Waugh, Partial time regressions as compared with individual trends, Econometrica 1 (1933), 387-401.

[9] J. Groß and S. Puntanen, Estimation under a general partitioned linear model, Linear Algebra and Its Applications 321 (2000), 131-144.

[10] M.C. Lovell, Seasonal adjustment of economic time series and multiple regression analysis, Journal of the American Statistical Association 58 (1963), 993-1010.

[11] G. Marsaglia and G.P.H. Styan, Equalities and inequalities for ranks of matrices, Linear and Multilinear Algebra 2 (1974), 269-292.

[12] M. Nurhonen and S. Puntanen, A property of partitioned generalized regression, Communications in Statistics, Theory and Methods 21 (1992), 1579-1583.

[13] S. Puntanen, Some matrix results related to a partitioned singular linearmodel, Communications in Statistics, Theory and Methods 25 (1996), 269-279.

[14] S. Puntanen, Some further results related to reduced singular linear models, Communications in Statistics, Theory and Methods 26 (1996), 375-385.

[15] S. Puntanen and G.P.H. Styan, The equality of the ordinary least squares estimator and the best linear unbiased estimator (with discussion), The American Statistician 43 (1989), 153-164.

[16] C.R. Rao, Unified theory of linear estimation, Sankhyā, Ser. A, 33 (1971), 371-394; Corrigenda, Sankhyā, Ser. A, 34, 194,477.

[17] C.R. Rao, Representations of best linear unbiased estimators in the Gauss-Markoff model with a singular dispersion matrix, Journal of Multivariate Analysis 3 (1973), 276-292.

[18] C.R. Rao, Projectors, generalized inverses and the BLUE's, Journal of the Royal Statistical Society, Ser. B 36 (1974), 442-448.