Non Regular Statistical Estimation
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Non Regular Statistical Estimation
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Author : Masafumi Akahira
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Non Regular Statistical Estimation written by Masafumi Akahira and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Non Regular Statistical Estimation
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Author : Masafumi Akahira
language : en
Publisher: Springer
Release Date : 1995-08-18
Non Regular Statistical Estimation written by Masafumi Akahira and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-08-18 with Mathematics categories.
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.
Non Regular Statistical Estimation
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Author : Masafumi Akahira
language : en
Publisher:
Release Date : 1995-08-18
Non Regular Statistical Estimation written by Masafumi Akahira and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-08-18 with categories.
Statistical Inference For Non Regular Family Of Distributions Unified Theory
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Author : Milind B. Bhatt
language : en
Publisher: Lulu.com
Release Date :
Statistical Inference For Non Regular Family Of Distributions Unified Theory written by Milind B. Bhatt and has been published by Lulu.com this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Statistical Estimation
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Author : I.A. Ibragimov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Statistical Estimation written by I.A. Ibragimov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.
when certain parameters in the problem tend to limiting values (for example, when the sample size increases indefinitely, the intensity of the noise ap proaches zero, etc.) To address the problem of asymptotically optimal estimators consider the following important case. Let X 1, X 2, ... , X n be independent observations with the joint probability density !(x,O) (with respect to the Lebesgue measure on the real line) which depends on the unknown patameter o e 9 c R1. It is required to derive the best (asymptotically) estimator 0:( X b ... , X n) of the parameter O. The first question which arises in connection with this problem is how to compare different estimators or, equivalently, how to assess their quality, in terms of the mean square deviation from the parameter or perhaps in some other way. The presently accepted approach to this problem, resulting from A. Wald's contributions, is as follows: introduce a nonnegative function w(0l> ( ), Ob Oe 9 (the loss function) and given two estimators Of and O! n 2 2 the estimator for which the expected loss (risk) Eown(Oj, 0), j = 1 or 2, is smallest is called the better with respect to Wn at point 0 (here EoO is the expectation evaluated under the assumption that the true value of the parameter is 0). Obviously, such a method of comparison is not without its defects.
Non Standard Spatial Statistics And Spatial Econometrics
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Author : Daniel A. Griffith
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-01-11
Non Standard Spatial Statistics And Spatial Econometrics written by Daniel A. Griffith and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-11 with Science categories.
Despite spatial statistics and spatial econometrics both being recent sprouts of the general tree "spatial analysis with measurement"—some may remember the debate after WWII about "theory without measurement" versus "measurement without theory"—several general themes have emerged in the pertaining literature. But exploring selected other fields of possible interest is tantalizing, and this is what the authors intend to report here, hoping that they will suscitate interest in the methodologies exposed and possible further applications of these methodologies. The authors hope that reactions about their publication will ensue, and they would be grateful to reader(s) motivated by some of the research efforts exposed hereafter letting them know about these experiences.
Non Regular Statistical Estimation Ii
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Author :
language : en
Publisher:
Release Date : 1986
Non Regular Statistical Estimation Ii written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with categories.
Statistical Estimation For Truncated Exponential Families
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Author : Masafumi Akahira
language : en
Publisher: Springer
Release Date : 2017-07-26
Statistical Estimation For Truncated Exponential Families written by Masafumi Akahira and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-26 with Mathematics categories.
This book presents new findings on nonregular statistical estimation. Unlike other books on this topic, its major emphasis is on helping readers understand the meaning and implications of both regularity and irregularity through a certain family of distributions. In particular, it focuses on a truncated exponential family of distributions with a natural parameter and truncation parameter as a typical nonregular family. This focus includes the (truncated) Pareto distribution, which is widely used in various fields such as finance, physics, hydrology, geology, astronomy, and other disciplines. The family is essential in that it links both regular and nonregular distributions, as it becomes a regular exponential family if the truncation parameter is known. The emphasis is on presenting new results on the maximum likelihood estimation of a natural parameter or truncation parameter if one of them is a nuisance parameter. In order to obtain more information on the truncation, the Bayesian approach is also considered. Further, the application to some useful truncated distributions is discussed. The illustrated clarification of the nonregular structure provides researchers and practitioners with a solid basis for further research and applications.
Nonparametric Methods In Statistics And Related Topics
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Author : Madan Lal Puri
language : en
Publisher: Walter de Gruyter
Release Date : 2013-02-06
Nonparametric Methods In Statistics And Related Topics written by Madan Lal Puri and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-06 with Mathematics categories.
No detailed description available for "Nonparametric Methods in Statistics and Related Topics".
Mathematical Statistics
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Author : Johann Pfanzagl
language : en
Publisher: Springer
Release Date : 2017-10-23
Mathematical Statistics written by Johann Pfanzagl and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-23 with Mathematics categories.
This book presents a detailed description of the development of statistical theory. In the mid twentieth century, the development of mathematical statistics underwent an enduring change, due to the advent of more refined mathematical tools. New concepts like sufficiency, superefficiency, adaptivity etc. motivated scholars to reflect upon the interpretation of mathematical concepts in terms of their real-world relevance. Questions concerning the optimality of estimators, for instance, had remained unanswered for decades, because a meaningful concept of optimality (based on the regularity of the estimators, the representation of their limit distribution and assertions about their concentration by means of Anderson’s Theorem) was not yet available. The rapidly developing asymptotic theory provided approximate answers to questions for which non-asymptotic theory had found no satisfying solutions. In four engaging essays, this book presents a detailed description of how the use of mathematical methods stimulated the development of a statistical theory. Primarily focused on methodology, questionable proofs and neglected questions of priority, the book offers an intriguing resource for researchers in theoretical statistics, and can also serve as a textbook for advanced courses in statisticc.