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Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition (Paperback, 2011 ed.): Haruo Yanai, Kei... Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition (Paperback, 2011 ed.)
Haruo Yanai, Kei Takeuchi, Yoshio Takane
R2,703 Discovery Miles 27 030 Ships in 10 - 15 working days

Aside from distribution theory, projections and the singular value decomposition (SVD) are the two most important concepts for understanding the basic mechanism of multivariate analysis. The former underlies the least squares estimation in regression analysis, which is essentially a projection of one subspace onto another, and the latter underlies principal component analysis, which seeks to find a subspace that captures the largest variability in the original space. This book is about projections and SVD. A thorough discussion of generalized inverse (g-inverse) matrices is also given because it is closely related to the former. The book provides systematic and in-depth accounts of these concepts from a unified viewpoint of linear transformations finite dimensional vector spaces. More specially, it shows that projection matrices (projectors) and g-inverse matrices can be defined in various ways so that a vector space is decomposed into a direct-sum of (disjoint) subspaces. Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition will be useful for researchers, practitioners, and students in applied mathematics, statistics, engineering, behaviormetrics, and other fields.

The Global Environment (Paperback, Softcover reprint of the original 1st ed. 1991): Kei Takeuchi, Masatoshi Yoshino The Global Environment (Paperback, Softcover reprint of the original 1st ed. 1991)
Kei Takeuchi, Masatoshi Yoshino
R1,549 Discovery Miles 15 490 Ships in 10 - 15 working days

The ffiM Japan International Symposium Energy and Environment - Global Warming was held in the Keidanren Guesthouse at the foot of Mt. Fuji, from October 21 to 24, 1990. The symposium was conducted in the context of ffiM Japan's longstanding commitment to good corporate citizenship. On this beautiful planet with its inter-dependent waters, lands and atmo sphere, we consider that the problems relating to the global environment are the most serious that the human race will face in the near future. The symposium provided an opportunity for forty scientists and researchers, from a wide variety of international backgrounds, to address matters relating to the global environment in an international forum. Eighteen papers were presented followed by panel and group discussions, on which the concluding remarks and recommendations are based. We chose three types of papers to target different aspects of the condition of the global environment: the natural science component; the socio-economic component; and the energy component which links these two. On the first day the symposium began with a plenary speech by Dr. J. Kondo followed by three keynote speeches, each with a particular focus. The following day, six speakers offered papers relating to the previous day's keynote speeches."

Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition (Hardcover, 2011 Ed.): Haruo Yanai, Kei... Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition (Hardcover, 2011 Ed.)
Haruo Yanai, Kei Takeuchi, Yoshio Takane
R2,973 Discovery Miles 29 730 Ships in 10 - 15 working days

Aside from distribution theory, projections and the singular value decomposition (SVD) are the two most important concepts for understanding the basic mechanism of multivariate analysis. The former underlies the least squares estimation in regression analysis, which is essentially a projection of one subspace onto another, and the latter underlies principal component analysis, which seeks to find a subspace that captures the largest variability in the original space. This book is about projections and SVD. A thorough discussion of generalized inverse (g-inverse) matrices is also given because it is closely related to the former. The book provides systematic and in-depth accounts of these concepts from a unified viewpoint of linear transformations finite dimensional vector spaces. More specially, it shows that projection matrices (projectors) and g-inverse matrices can be defined in various ways so that a vector space is decomposed into a direct-sum of (disjoint) subspaces. Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition will be useful for researchers, practitioners, and students in applied mathematics, statistics, engineering, behaviormetrics, and other fields.

Non-Regular Statistical Estimation (Paperback, Softcover reprint of the original 1st ed. 1995): Masafumi Akahira, Kei Takeuchi Non-Regular Statistical Estimation (Paperback, Softcover reprint of the original 1st ed. 1995)
Masafumi Akahira, Kei Takeuchi
R1,525 Discovery Miles 15 250 Ships in 10 - 15 working days

In order to obtain many of the classical results in the theory of statistical estimation, it is usual to impose regularity conditions on the distributions under consideration. In small sample and large sample theories of estimation there are well established sets of regularity conditions, and it is worth while to examine what may follow if any one of these regularity conditions fail to hold. "Non-regular estimation" literally means the theory of statistical estimation when some or other of the regularity conditions fail to hold. In this monograph, the authors present a systematic study of the meaning and implications of regularity conditions, and show how the relaxation of such conditions can often lead to surprising conclusions. Their emphasis is on considering small sample results and to show how pathological examples may be considered in this broader framework.

Asymptotic Efficiency of Statistical Estimators: Concepts and Higher Order Asymptotic Efficiency - Concepts and Higher Order... Asymptotic Efficiency of Statistical Estimators: Concepts and Higher Order Asymptotic Efficiency - Concepts and Higher Order Asymptotic Efficiency (Paperback, Softcover reprint of the original 1st ed. 1981)
Masafumi Akahira, Kei Takeuchi
R1,541 Discovery Miles 15 410 Ships in 10 - 15 working days

This monograph is a collection of results recently obtained by the authors. Most of these have been published, while others are awaitlng publication. Our investigation has two main purposes. Firstly, we discuss higher order asymptotic efficiency of estimators in regular situa tions. In these situations it is known that the maximum likelihood estimator (MLE) is asymptotically efficient in some (not always specified) sense. However, there exists here a whole class of asymptotically efficient estimators which are thus asymptotically equivalent to the MLE. It is required to make finer distinctions among the estimators, by considering higher order terms in the expansions of their asymptotic distributions. Secondly, we discuss asymptotically efficient estimators in non regular situations. These are situations where the MLE or other estimators are not asymptotically normally distributed, or where l 2 their order of convergence (or consistency) is not n /, as in the regular cases. It is necessary to redefine the concept of asympto tic efficiency, together with the concept of the maximum order of consistency. Under the new definition as asymptotically efficient estimator may not always exist. We have not attempted to tell the whole story in a systematic way. The field of asymptotic theory in statistical estimation is relatively uncultivated. So, we have tried to focus attention on such aspects of our recent results which throw light on the area."

Contributions on Theory of Mathematical Statistics (Hardcover, 1st ed. 2020): Kei Takeuchi Contributions on Theory of Mathematical Statistics (Hardcover, 1st ed. 2020)
Kei Takeuchi
R4,311 Discovery Miles 43 110 Ships in 10 - 15 working days

This volume is a reorganized edition of Kei Takeuchi's works on various problems in mathematical statistics based on papers and monographs written since the 1960s on several topics in mathematical statistics and published in various journals in English and in Japanese. They are organized into seven parts, each of which is concerned with specific topics and edited to make a consistent thesis. Sometimes expository chapters have been added. The topics included are as follows: theory of statistical prediction from a non-Bayesian viewpoint and analogous to the classical theory of statistical inference; theory of robust estimation, concepts, and procedures, and its implications for practical applications; theory of location and scale covariant/invariant estimations with derivation of explicit forms in various cases; theory of selection and testing of parametric models and a comprehensive approach including the derivation of the Akaike's Information Criterion (AIC); theory of randomized designs, comparisons of random and conditional approaches, and of randomized and non-randomized designs, with random sampling from finite populations considered as a special case of randomized designs and with some separate independent papers included. Theory of asymptotically optimal and higher-order optimal estimators are not included, since most of them already have been published in the Joint Collected Papers of M. Akahira and K. Takeuchi. There are some topics that are not necessarily new, do not seem to have attracted many theoretical statisticians, and do not appear to have been systematically dealt with in textbooks or expository monographs. One purpose of this volume is to give a comprehensive view of such problems as well.

A Test of Normality - Especially Against Symmetric Alternatives (Paperback): Kei Takeuchi A Test of Normality - Especially Against Symmetric Alternatives (Paperback)
Kei Takeuchi
R362 Discovery Miles 3 620 Ships in 10 - 15 working days
On a Problem of Fixing the Level of Independent Variables in a Linear Regression Function (Hardcover): Kei Takeuchi On a Problem of Fixing the Level of Independent Variables in a Linear Regression Function (Hardcover)
Kei Takeuchi
R719 Discovery Miles 7 190 Ships in 10 - 15 working days
A Uniformly Asymptotically Efficient Robust Estimator of a Location Parameter (Hardcover): Kei Takeuchi A Uniformly Asymptotically Efficient Robust Estimator of a Location Parameter (Hardcover)
Kei Takeuchi
R793 Discovery Miles 7 930 Ships in 10 - 15 working days
Minimax Linear Predictor Under Lipschitz' Type Conditions for the Regression Function (Hardcover): Kei Takeuchi Minimax Linear Predictor Under Lipschitz' Type Conditions for the Regression Function (Hardcover)
Kei Takeuchi
R724 Discovery Miles 7 240 Ships in 10 - 15 working days
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