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...

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...

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...

This valuable reference on projectors, generalized inverses, and SVD covers concepts numerous cutting-edge concepts and provides systematic and in-depth accounts of these ideas from the viewpoint of linear transformations of finite dimensional vector spaces.

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...

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 six 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...

Masafumi Akahira and Kei Takeuchi have collaborated in research on mathematical statistics for nearly 30 years. This volume is a collection of their papers, covering the theory of estimation, such as asymptotic, non-regular, and sequential.