Characterizations of the best linear unbiased estimator in the general Gauss-Markov model with the use of matrix partial orderings

AbstractUnder the general Gauss-Markov model {Y, Xβ, σ2V}, two new characterizations of BLUE(Xβ) are derived involving the Löwner and rank-subtractivity partial orderings between the dispersion matrix of BLUE(Xβ) and the dispersion matrix of Y. As particular cases of these characterizations, three new criteria for the equality between OLSE(Xβ) and BLUE(Xβ) are given

Personal photographic glimpses of Professor Bikas Kumar Sinha: The Bikas Kumar Sinha Endowment Lecture

My goal in this Endowment Lecture is to provide some glimpses of Professor Bikas Sinha, based on 30 years of friendship and appreciation. In particular I’ll emphasize Bikas’ remarkable impact as a demanding but inspiring mentor and collaborator of several doctoral students of Tampere University; among them, Arto Luoma, Laura Koskela, Anne Puustelli, Klaus Nordhausen, Jarkko Isotalo and Sami Helle; and extremely active and productive co-operation with Erkki Liski and Tapio Nummi and their research group. On my personal side I’ll go through, with photographic illustrations, some highlights like visiting Bikas’ residence and family in Kolkata on the 3rd of January 1995; visits to our home in Nokia; international scientific meetings like in Kolkata, Hyderabad and in Bedlewo, Poland, and the guided tour in Kolkata Botanical Gardens on the 2nd of January 2013.publishedVersionNon peer reviewe

The efficiency factorization multiplier for the Watson efficiency in partitioned linear models: some examples and a literature review

We consider partitioned linear models where the model matrix X = (X1 : X2) has full column rank, and concentrate on the special case whereX0 1X2 = 0 when we say that the model is orthogonally partitioned. We assume that the underlying covariance matrix is positive definite and introduce the efficiency factorization multiplier which relates the total Watson efficiency of ordinary least squares to the product of the two subset Watson efficiencies. We illustrate our findings with several examples and present a literature review

All about the ⊥ with its applications in the linear statistical models

For an n x m real matrix A the matrix A⊥ is defined as a matrix spanning the orthocomplement of the column space of A, when the orthogonality is defined with respect to the standard inner product ⟨x, y⟩ = x'y. In this paper we collect together various properties of the ⊥ operation and its applications in linear statistical models. Results covering the more general inner products are also considered. We also provide a rather extensive list of reference

The Legend of the Equality of OLSE and BLUE: Highlighted by C.R. Rao in 1967

Peer reviewe