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Asymptotic Theory Of Statistical Inference


Asymptotic Theory Of Statistical Inference
Author: B. L. S. Prakasa Rao
Publisher: John Wiley & Sons Incorporated
ISBN:
Size: 48.54 MB
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Probability and stochastic processes; Limit theorems for some statistics; Asymptotic theory of estimation; Linear parametric inference; Martingale approach to inference; Inference in nonlinear regression; Von mises functionals; Empirical characteristic function and its applications.




Asymptotic Theory Of Statistical Inference For Time Series


Asymptotic Theory Of Statistical Inference
Author: Masanobu Taniguchi
Publisher: Springer Science & Business Media
ISBN: 146121162X
Size: 65.26 MB
Format: PDF, Docs
View: 4764
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The primary aim of this book is to provide modern statistical techniques and theory for stochastic processes. The stochastic processes mentioned here are not restricted to the usual AR, MA, and ARMA processes. A wide variety of stochastic processes, including non-Gaussian linear processes, long-memory processes, nonlinear processes, non-ergodic processes and diffusion processes are described. The authors discuss estimation and testing theory and many other relevant statistical methods and techniques.




Asymptotic Statistical Inference


Asymptotic Theory Of Statistical Inference
Author: Shailaja Deshmukh
Publisher: Springer
ISBN: 9789811590023
Size: 46.34 MB
Format: PDF, Kindle
View: 7098
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The book presents the fundamental concepts from asymptotic statistical inference theory, elaborating on some basic large sample optimality properties of estimators and some test procedures. The most desirable property of consistency of an estimator and its large sample distribution, with suitable normalization, are discussed, the focus being on the consistent and asymptotically normal (CAN) estimators. It is shown that for the probability models belonging to an exponential family and a Cramer family, the maximum likelihood estimators of the indexing parameters are CAN. The book describes some large sample test procedures, in particular, the most frequently used likelihood ratio test procedure. Various applications of the likelihood ratio test procedure are addressed, when the underlying probability model is a multinomial distribution. These include tests for the goodness of fit and tests for contingency tables. The book also discusses a score test and Wald’s test, their relationship with the likelihood ratio test and Karl Pearson’s chi-square test. An important finding is that, while testing any hypothesis about the parameters of a multinomial distribution, a score test statistic and Karl Pearson’s chi-square test statistic are identical. Numerous illustrative examples of differing difficulty level are incorporated to clarify the concepts. For better assimilation of the notions, various exercises are included in each chapter. Solutions to almost all the exercises are given in the last chapter, to motivate students towards solving these exercises and to enable digestion of the underlying concepts. The concepts from asymptotic inference are crucial in modern statistics, but are difficult to grasp in view of their abstract nature. To overcome this difficulty, keeping up with the recent trend of using R software for statistical computations, the book uses it extensively, for illustrating the concepts, verifying the properties of estimators and carrying out various test procedures. The last section of the chapters presents R codes to reveal and visually demonstrate the hidden aspects of different concepts and procedures. Augmenting the theory with R software is a novel and a unique feature of the book. The book is designed primarily to serve as a text book for a one semester introductory course in asymptotic statistical inference, in a post-graduate program, such as Statistics, Bio-statistics or Econometrics. It will also provide sufficient background information for studying inference in stochastic processes. The book will cater to the need of a concise but clear and student-friendly book introducing, conceptually and computationally, basics of asymptotic inference.




Asymptotic Theory Of Quantum Statistical Inference


Asymptotic Theory Of Statistical Inference
Author: Masahito Hayashi
Publisher: World Scientific
ISBN: 981448198X
Size: 29.38 MB
Format: PDF, Mobi
View: 6955
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' Quantum statistical inference, a research field with deep roots in the foundations of both quantum physics and mathematical statistics, has made remarkable progress since 1990. In particular, its asymptotic theory has been developed during this period. However, there has hitherto been no book covering this remarkable progress after 1990; the famous textbooks by Holevo and Helstrom deal only with research results in the earlier stage (1960s-1970s). This book presents the important and recent results of quantum statistical inference. It focuses on the asymptotic theory, which is one of the central issues of mathematical statistics and had not been investigated in quantum statistical inference until the early 1980s. It contains outstanding papers after Holevo's textbook, some of which are of great importance but are not available now. The reader is expected to have only elementary mathematical knowledge, and therefore much of the content will be accessible to graduate students as well as research workers in related fields. Introductions to quantum statistical inference have been specially written for the book. Asymptotic Theory of Quantum Statistical Inference: Selected Papers will give the reader a new insight into physics and statistical inference. Contents:Hypothesis TestingQuantum Cramér-Rao Bound in Mixed States ModelQuantum Cramér-Rao Bound in Pure States ModelGroup Symmetric Approach to Pure States ModelLarge Deviation Theory in Quantum EstimationFuther Topics on Quantum Statistical Inference Readership: Graduate students in quantum physics, mathematical physics, and probability and statistics. Keywords:Quantum Information;Estimation Theory;Statistics;Statistical Inference;Mathematical Physics;Asymptotic Theory;Hypothesis TestingReviews:“This book will give the scholars new insight into physics and statistical inference.”Zentralblatt MATH '



Asymptotic Theory of Statistical Inference
Language: en
Pages: 438
Authors: B. L. S. Prakasa Rao, Bhagavatula Lakshmi Surya PrakasaRao
Categories: Mathematics
Type: BOOK - Published: 1987-01-16 - Publisher: John Wiley & Sons Incorporated
Probability and stochastic processes; Limit theorems for some statistics; Asymptotic theory of estimation; Linear parametric inference; Martingale approach to inference; Inference in nonlinear regression; Von mises functionals; Empirical characteristic function and its applications.
Asymptotic Theory of Statistical Inference for Time Series
Language: en
Pages: 662
Authors: Masanobu Taniguchi, Yoshihide Kakizawa
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media
The primary aim of this book is to provide modern statistical techniques and theory for stochastic processes. The stochastic processes mentioned here are not restricted to the usual AR, MA, and ARMA processes. A wide variety of stochastic processes, including non-Gaussian linear processes, long-memory processes, nonlinear processes, non-ergodic processes and
Asymptotic Theory of Quantum Statistical Inference
Language: en
Pages: 560
Authors: Masahito Hayashi
Categories: Science
Type: BOOK - Published: 2005-02-21 - Publisher: World Scientific
' Quantum statistical inference, a research field with deep roots in the foundations of both quantum physics and mathematical statistics, has made remarkable progress since 1990. In particular, its asymptotic theory has been developed during this period. However, there has hitherto been no book covering this remarkable progress after 1990;
Asymptotic Theory of Statistical Inference for Stochastic Processes
Language: en
Pages:
Authors: B. L. S. Prakasa Rao
Categories: Science
Type: BOOK - Published: 1979 - Publisher:
Books about Asymptotic Theory of Statistical Inference for Stochastic Processes
Asymptotic Statistical Inference
Language: en
Pages: 529
Authors: Shailaja Deshmukh, Madhuri Kulkarni
Categories: Mathematics
Type: BOOK - Published: 2021-07-05 - Publisher: Springer Nature
The book presents the fundamental concepts from asymptotic statistical inference theory, elaborating on some basic large sample optimality properties of estimators and some test procedures. The most desirable property of consistency of an estimator and its large sample distribution, with suitable normalization, are discussed, the focus being on the consistent