The Coordinate Free Approach to Gauss Markov Estimation

The Coordinate Free Approach to Gauss Markov Estimation

Coordinate-free methods are not new in Gauss-Markov estimation, besides Seber the work of Kolmogorov [11], SCheffe [36], Kruskal [21], [22] and Malinvaud [25], [26] should be mentioned.

Author: H. Drygas

Publisher: Springer Science & Business Media

ISBN: 9783642651489

Category: Business & Economics

Page: 118

View: 653

These notes originate from a couple of lectures which were given in the Econometric Workshop of the Center for Operations Research and Econometrics (CORE) at the Catholic University of Louvain. The participants of the seminars were recommended to read the first four chapters of Seber's book [40], but the exposition of the material went beyond Seber's exposition, if it seemed necessary. Coordinate-free methods are not new in Gauss-Markov estimation, besides Seber the work of Kolmogorov [11], SCheffe [36], Kruskal [21], [22] and Malinvaud [25], [26] should be mentioned. Malinvaud's approach however is a little different from that of the other authors, because his optimality criterion is based on the ellipsoid of c- centration. This criterion is however equivalent to the usual c- cept of minimal covariance-matrix and therefore the result must be the same in both cases. While the usual theory gives no indication how small the covariance-matrix can be made before the optimal es timator is computed, Malinvaud can show how small the ellipsoid of concentration can be made: it is at most equal to the intersection of the ellipssoid of concentration of the observed random vector and the linear space in which the (unknown) expectation value of the observed random vector is lying. This exposition is based on the observation, that in regression ~nalysis and related fields two conclusions are or should preferably be applied repeatedly.
Categories: Business & Economics

Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability

Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability

WILLIAM KRUSKAL , The coordinate - free approach to Gauss - Markov estimation , and its application to missing and extra observations . D. V. LINDLEY , The use of prior probability distributions in statistical inference and decisions .

Author: Jerzy Neyman

Publisher: Univ of California Press

ISBN:

Category: Mathematical statistics

Page: 413

View: 775

Categories: Mathematical statistics

Bilinear Regression Analysis

Bilinear Regression Analysis

This topic has a long history within the GaussMarkov model framework (see Puntanen et al., 2011, Chapter 10; Haslett et al., 2014). ... Gauss-Markov estimation for multivariate linear models: A coordinate free approach.

Author: Dietrich von Rosen

Publisher: Springer

ISBN: 9783319787848

Category: Mathematics

Page: 468

View: 137

This book expands on the classical statistical multivariate analysis theory by focusing on bilinear regression models, a class of models comprising the classical growth curve model and its extensions. In order to analyze the bilinear regression models in an interpretable way, concepts from linear models are extended and applied to tensor spaces. Further, the book considers decompositions of tensor products into natural subspaces, and addresses maximum likelihood estimation, residual analysis, influential observation analysis and testing hypotheses, where properties of estimators such as moments, asymptotic distributions or approximations of distributions are also studied. Throughout the text, examples and several analyzed data sets illustrate the different approaches, and fresh insights into classical multivariate analysis are provided. This monograph is of interest to researchers and Ph.D. students in mathematical statistics, signal processing and other fields where statistical multivariate analysis is utilized. It can also be used as a text for second graduate-level courses on multivariate analysis.
Categories: Mathematics

Matrix Tricks for Linear Statistical Models

Matrix Tricks for Linear Statistical Models

Estimation and Inference in Econometrics. Oxford University Press. ... The Kalman filter from the perspective of Goldberger–Theil estimators. ... GaussMarkov estimation for multivariate linear models: A coordinate free approach.

Author: Simo Puntanen

Publisher: Springer Science & Business Media

ISBN: 9783642104732

Category: Mathematics

Page: 486

View: 487

In teaching linear statistical models to first-year graduate students or to final-year undergraduate students there is no way to proceed smoothly without matrices and related concepts of linear algebra; their use is really essential. Our experience is that making some particular matrix tricks very familiar to students can substantially increase their insight into linear statistical models (and also multivariate statistical analysis). In matrix algebra, there are handy, sometimes even very simple “tricks” which simplify and clarify the treatment of a problem—both for the student and for the professor. Of course, the concept of a trick is not uniquely defined—by a trick we simply mean here a useful important handy result. In this book we collect together our Top Twenty favourite matrix tricks for linear statistical models.
Categories: Mathematics

Applied and Computational Matrix Analysis

Applied and Computational Matrix Analysis

Drygas, H.: The Coordinate-Free Approach to Gauss-Markov Estimation. Springer, Berlin (1970) Drygas, H.: Sufficiency and completeness in the general Gauss-Markov model. Sankhy ̄a Ser. A 45, 88–98 (1983) Groß, J.: A note on the concepts ...

Author: Natália Bebiano

Publisher: Springer

ISBN: 9783319499840

Category: Mathematics

Page: 347

View: 206

This volume presents recent advances in the field of matrix analysis based on contributions at the MAT-TRIAD 2015 conference. Topics covered include interval linear algebra and computational complexity, Birkhoff polynomial basis, tensors, graphs, linear pencils, K-theory and statistic inference, showing the ubiquity of matrices in different mathematical areas. With a particular focus on matrix and operator theory, statistical models and computation, the International Conference on Matrix Analysis and its Applications 2015, held in Coimbra, Portugal, was the sixth in a series of conferences. Applied and Computational Matrix Analysis will appeal to graduate students and researchers in theoretical and applied mathematics, physics and engineering who are seeking an overview of recent problems and methods in matrix analysis.
Categories: Mathematics

Statistical Data Analysis and Inference

Statistical Data Analysis and Inference

Statist. Soc. Ser. B 25, 124-127. Drygas, H. (1970). The Coordinate-Free Approach to Gauss-Markov Estimation. Springer, Berlin. Drygas, H. (1983). Sufficiency and completeness in the general Gauss-Markov model. Sankhyā Ser. A 45, 88–98.

Author: Y. Dodge

Publisher: Elsevier

ISBN: 9781483296111

Category: Mathematics

Page: 630

View: 134

A wide range of topics and perspectives in the field of statistics are brought together in this volume. The contributions originate from invited papers presented at an international conference which was held in honour of C. Radhakrishna Rao, one of the most eminent statisticians of our time and a distinguished scientist.
Categories: Mathematics

Probability and Statistical Inference

Probability and Statistical Inference

REFERENCES 1 Drygas H. (1970): The Coordinate-free Approach to GaussMarkov Estimation. Lecture Notes in Operations Research and Mathematical Systems vol. 40. Springer-Verlaq 1970. 2 Haberman S.J. (1975): How much do Gauss-Markov and ...

Author: Wilfried Grossmann

Publisher: Springer Science & Business Media

ISBN: 9789400978409

Category: Mathematics

Page: 390

View: 167

The interaction of various ideas from different researchers provides a main impetus to mathematical prosress. An important way to make communication possible is through international conferences on more or less spezialized topics~ The existence of several centers for research in probabil ity and statistics in the eastern part of central Europe - somewhat vaguely described as the Pannonian area - led to the idea of organizing Pannonian Symposia on Mathematical Statistics (PS~1S). The second such symposium was held at Bad Tatzmannsdorf, Burgenland (Austria), from 14 to 20 June 1981. About 100 researchers from 13 countries participated in that event and about 70 papers were delivered. Most of the papers dealt with one of the following topics: nonparametric estimation theory, asymptotic theory of estimation, invariance principles, limit theorems and aoplications. Full versions of selected papers, all presenting new results are included in this volume. The editors take this opportunity to thank the following institutions for their assistance in making the conference possible: the Provincial Government of Burgenland, the Austrian Ministry for Research and Science, the Burgenland Chamber of Commerce, the Control Data Corporation, the Austrian Society for Statistics and Informatics, the Landes hypothekenbank Burgenland, the Volksbank Oberwart, and the Community and Kurbad AG of Bad Tatzmannsdorf. We are also greatly indebted to all those persons who helped in editing this volume and in particular to the vii W. Grossmann et al. reds.), Probability and Statistical Inference, vii-viii.
Categories: Mathematics

Methodology and Applications of Statistics

Methodology and Applications of Statistics

... S.: Characterizations of the best linear unbiased estimator in the general Gauss-Markov model with the use of matrix partial orderings. ... M.L.: GaussMarkov estimation for multivariate linear models: a coordinate free approach.

Author: Barry C. Arnold

Publisher: Springer Nature

ISBN: 9783030836702

Category: Electronic books

Page: 447

View: 651

Dedicated to one of the most outstanding researchers in the field of statistics, this volume in honor of C.R. Rao, on the occasion of his 100th birthday, provides a birds-eye view of a broad spectrum of research topics, paralleling C.R. Raos wide-ranging research interests. The books contributors comprise a representative sample of the countless number of researchers whose careers have been influenced by C.R. Rao, through his work or his personal aid and advice. As such, written by experts from more than 15 countries, the books original and review contributions address topics including statistical inference, distribution theory, estimation theory, multivariate analysis, hypothesis testing, statistical modeling, design and sampling, shape and circular analysis, and applications. The book will appeal to statistics researchers, theoretical and applied alike, and PhD students. Happy Birthday, C.R. Rao!
Categories: Electronic books

Multivariate Multilinear and Mixed Linear Models

Multivariate  Multilinear and Mixed Linear Models

Dong, B., Guo, W., Tian, Y.: On relations between BLUEs under two transformed linear models. J. Multivariate Anal. 13, 279–292 (2014) 25. Drygas, H.: The Coordinate-Free Approach to Gauss-Markov Estimation. Springer, Berlin (1970) 26.

Author: Katarzyna Filipiak

Publisher: Springer Nature

ISBN: 9783030754945

Category: Mathematics

Page: 350

View: 646

This book presents the latest findings on statistical inference in multivariate, multilinear and mixed linear models, providing a holistic presentation of the subject. It contains pioneering and carefully selected review contributions by experts in the field and guides the reader through topics related to estimation and testing of multivariate and mixed linear model parameters. Starting with the theory of multivariate distributions, covering identification and testing of covariance structures and means under various multivariate models, it goes on to discuss estimation in mixed linear models and their transformations. The results presented originate from the work of the research group Multivariate and Mixed Linear Models and their meetings held at the Mathematical Research and Conference Center in Będlewo, Poland, over the last 10 years. Featuring an extensive bibliography of related publications, the book is intended for PhD students and researchers in modern statistical science who are interested in multivariate and mixed linear models.
Categories: Mathematics