Masafumi Akahira and Kei Takeuchi have collaborated in research on mathematical statistics for nearly thirty years and have published many articles and papers. This volume is a collection of their papers, some published in well-known and others in lesser-known journals. The papers cover various fields, but the main subject is the theory of estimation -- asymptotic, non-regular, sequential, etc. All the papers are theoretical in nature, but have implications for applied problems.
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.
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.
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.
In order to protect Natsuo, Hina vanishes without a trace. As Natsuo wastes away with a broken heart, not even Rui can reach him. Then, in order to pull himself out of the depths of despair, Natsuo makes a decision that will change his life forever…
Recent debates about sustainable development have shifted their focus from fixing environmental problems in a technocratic and economic way to more fundamental changes in social-political processes and relations. In this context, participation is a genuinely transformative approach to sustainable development, yet the process by which participation leads to transformation is not sufficiently understood. This book considers how the act of participating in sustainable development projects can bring about social transformation that is considered to be fair and just by the participants and non-participants in a broader societal context. Drawing on ideas from social theory and applied anthropology, the book proposes a reflexivity-based framework to analyse participation as a type of social action underpinned by primary experience. Development projects have a transformative effect when participants are given the opportunity to reflect on their experience, share the reflection with others, and open new space for collective deliberation and change. The book applies this framework to assess community-based participatory projects in the Amazon, African slums and rural settlements, and disaster stricken areas in Japan. It also outlines potential institutions of governance to institutionalize the change by referring to current food governance, drawing out lessons with international relevance. This book will be of interest to students of sustainable development, environmental policy and development studies, as well as practitioners and policy-makers in these fields.
Cosmeceuticals are the latest additions to the health industry and have an ever-expanding market. They are considered to be a marriage between cosmetics and drugs and are defined as preparations applied on the body that may modify the physiological functions of the skin. However, as more cosmeceuticals are being launched in the market and more types of drugs are incorporated into the formulation, the composition of cosmeceuticals is becoming more complex. Handbook of Cosmeceutical Excipients and their Safeties summarises the current evidence relating to cosmeceuticals' side effects and highlights the important information that practitioners and consumers need to know, as well as ways to avoid the adverse effects of the excipients. Handbook of Cosmeceutical Excipients and their Safeties includes chapters covering topics such as the history of cosmeceuticals and the laws that regulate them, skin permeation, carcinogenicity as a systemic adverse effect and dermatitis as a topical adverse effect. It concludes with an appendix that gives brief information on the potency and permeability of common ingredients in cosmeceuticals. The appendix aims to highlight the maximum allowable quantity of each ingredient to ensure product safety for consumers. The appendix was prepared by compiling the ingredients of 257 products containing more than 500 compounds, collected from a hospital pharmacy in Singapore. - Focuses on the practical aspect of adverse effects from cosmeceuticals - Explains the regulatory framework of cosmeceuticals - Gives an idea of how excipients and drugs in cosmeceuticals enter the skin and methods of control
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.
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.
This will help us customize your experience to showcase the most relevant content to your age group
Please select from below
Login
Not registered?
Sign up
Already registered?
Success – Your message will goes here
We'd love to hear from you!
Thank you for visiting our website. Would you like to provide feedback on how we could improve your experience?
This site does not use any third party cookies with one exception — it uses cookies from Google to deliver its services and to analyze traffic.Learn More.