Parameter Estimation and Hypothesis Testing in Spectral Analysis of Stationary Time Series
Parameter Estimation and Hypothesis Testing in Spectral Analysis of Stationary Time Series

Author: K. Dzhaparidze

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 331

ISBN-13: 1461248426

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. . ) (under the assumption that the spectral density exists). For this reason, a vast amount of periodical and monographic literature is devoted to the nonparametric statistical problem of estimating the function tJ( T) and especially that of leA) (see, for example, the books [4,21,22,26,56,77,137,139,140,]). However, the empirical value t;; of the spectral density I obtained by applying a certain statistical procedure to the observed values of the variables Xl' . . . , X , usually depends in n a complicated manner on the cyclic frequency). . This fact often presents difficulties in applying the obtained estimate t;; of the function I to the solution of specific problems rela ted to the process X . Theref ore, in practice, the t obtained values of the estimator t;; (or an estimator of the covariance function tJ~( T» are almost always "smoothed," i. e. , are approximated by values of a certain sufficiently simple function 1 = 1

Handbook of Nanoscopy, 2 Volume Set
Handbook of Nanoscopy, 2 Volume Set

Author: Gustaaf van Tendeloo

Publisher: John Wiley & Sons

Published: 2012-05-21

Total Pages: 1484

ISBN-13: 3527317066

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This completely revised successor to the Handbook of Microscopy supplies in-depth coverage of all imaging technologies from the optical to the electron and scanning techniques. Adopting a twofold approach, the book firstly presents the various technologies as such, before going on to cover the materials class by class, analyzing how the different imaging methods can be successfully applied. It covers the latest developments in techniques, such as in-situ TEM, 3D imaging in TEM and SEM, as well as a broad range of material types, including metals, alloys, ceramics, polymers, semiconductors, minerals, quasicrystals, amorphous solids, among others. The volumes are divided between methods and applications, making this both a reliable reference and handbook for chemists, physicists, biologists, materials scientists and engineers, as well as graduate students and their lecturers.

Parameter Estimation and Hypothesis Testing in Spectral Analysis of Stationary Time Series
Parameter Estimation and Hypothesis Testing in Spectral Analysis of Stationary Time Series

Author: K. Dzhaparidze

Publisher: Springer Science & Business Media

Published: 1986

Total Pages: 346

ISBN-13: 9780387961415

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. . ) (under the assumption that the spectral density exists). For this reason, a vast amount of periodical and monographic literature is devoted to the nonparametric statistical problem of estimating the function tJ( T) and especially that of leA) (see, for example, the books [4,21,22,26,56,77,137,139,140,]). However, the empirical value t;; of the spectral density I obtained by applying a certain statistical procedure to the observed values of the variables Xl' . . . , X , usually depends in n a complicated manner on the cyclic frequency). . This fact often presents difficulties in applying the obtained estimate t;; of the function I to the solution of specific problems rela ted to the process X . Theref ore, in practice, the t obtained values of the estimator t;; (or an estimator of the covariance function tJ~( T» are almost always "smoothed," i. e. , are approximated by values of a certain sufficiently simple function 1 = 1

Mathematical Models for Speech Technology
Mathematical Models for Speech Technology

Author: Stephen Levinson

Publisher: John Wiley & Sons

Published: 2005-05-13

Total Pages: 282

ISBN-13: 0470020903

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Mathematical Models of Spoken Language presents the motivations for, intuitions behind, and basic mathematical models of natural spoken language communication. A comprehensive overview is given of all aspects of the problem from the physics of speech production through the hierarchy of linguistic structure and ending with some observations on language and mind. The author comprehensively explores the argument that these modern technologies are actually the most extensive compilations of linguistic knowledge available.Throughout the book, the emphasis is on placing all the material in a mathematically coherent and computationally tractable framework that captures linguistic structure. It presents material that appears nowhere else and gives a unification of formalisms and perspectives used by linguists and engineers. Its unique features include a coherent nomenclature that emphasizes the deep connections amongst the diverse mathematical models and explores the methods by means of which they capture linguistic structure. This contrasts with some of the superficial similarities described in the existing literature; the historical background and origins of the theories and models; the connections to related disciplines, e.g. artificial intelligence, automata theory and information theory; an elucidation of the current debates and their intellectual origins; many important little-known results and some original proofs of fundamental results, e.g. a geometric interpretation of parameter estimation techniques for stochastic models and finally the author's own unique perspectives on the future of this discipline. There is a vast literature on Speech Recognition and Synthesis however, this book is unlike any other in the field. Although it appears to be a rapidly advancing field, the fundamentals have not changed in decades. Most of the results are presented in journals from which it is difficult to integrate and evaluate all of these recent ideas. Some of the fundamentals have been collected into textbooks, which give detailed descriptions of the techniques but no motivation or perspective. The linguistic texts are mostly descriptive and pictorial, lacking the mathematical and computational aspects. This book strikes a useful balance by covering a wide range of ideas in a common framework. It provides all the basic algorithms and computational techniques and an analysis and perspective, which allows one to intelligently read the latest literature and understand state-of-the-art techniques as they evolve.

Parameter Estimation and Inverse Problems
Parameter Estimation and Inverse Problems

Author: Richard C. Aster

Publisher: Academic Press

Published: 2013

Total Pages: 377

ISBN-13: 0123850487

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Preface -- 1. Introduction -- 2. Linear Regression -- 3. Discretizing Continuous Inverse Problems -- 4. Rank Deficiency and Ill-Conditioning -- 5. Tikhonov Regularization -- 6. Iterative Methods -- 7. Other Regularization Techniques -- 8. Fourier Techniques -- 9. Nonlinear Regression -- 10. Nonlinear Inverse Problems -- 11. Bayesian Methods -- Appendix A: Review of Linear Algebra -- Appendix B: Review of Probability and Statistics -- Appendix C: Glossary of Notation -- Bibliography -- IndexLinear Regression -- Discretizing Continuous Inverse Problems -- Rank Deficiency and Ill-Conditioning -- Tikhonov Regularization -- Iterative Methods -- Other Regularization Techniques -- Fourier Techniques -- Nonlinear Regression -- Nonlinear Inverse Problems -- Bayesian Methods.

Empirical Likelihood and Quantile Methods for Time Series
Empirical Likelihood and Quantile Methods for Time Series

Author: Yan Liu

Publisher: Springer

Published: 2018-12-05

Total Pages: 144

ISBN-13: 9811001529

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This book integrates the fundamentals of asymptotic theory of statistical inference for time series under nonstandard settings, e.g., infinite variance processes, not only from the point of view of efficiency but also from that of robustness and optimality by minimizing prediction error. This is the first book to consider the generalized empirical likelihood applied to time series models in frequency domain and also the estimation motivated by minimizing quantile prediction error without assumption of true model. It provides the reader with a new horizon for understanding the prediction problem that occurs in time series modeling and a contemporary approach of hypothesis testing by the generalized empirical likelihood method. Nonparametric aspects of the methods proposed in this book also satisfactorily address economic and financial problems without imposing redundantly strong restrictions on the model, which has been true until now. Dealing with infinite variance processes makes analysis of economic and financial data more accurate under the existing results from the demonstrative research. The scope of applications, however, is expected to apply to much broader academic fields. The methods are also sufficiently flexible in that they represent an advanced and unified development of prediction form including multiple-point extrapolation, interpolation, and other incomplete past forecastings. Consequently, they lead readers to a good combination of efficient and robust estimate and test, and discriminate pivotal quantities contained in realistic time series models.