Adapting Local Minimax Theory To Modern Applications PDF Download
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| Author | : Feng Ruan |
| Publisher | : |
| Total Pages | : |
| Release | : 2019 |
| Genre | : |
| ISBN | : |
Download Adapting Local Minimax Theory to Modern Applications Book in PDF, ePub and Kindle
Maximum likelihood estimation (MLE) is influential because it can be easily applied to generate optimal, statistically efficient procedures for broad classes of estimation problems. Nonetheless, the theory does not apply to modern settings—such as problems with computational, communication, or privacy considerations—where our estimators have resource constraints. The thesis will introduce a modern maximum likelihood theory (through generalization of local minimax theory) that addresses these issues, focusing specifically on procedures that must be computationally efficient or privacy-preserving. To do so, I first derive analogues of Fisher information for these applications, which allows a precise characterization of tradeoffs between statistical efficiency, privacy, and computation. To complete the development, I also describe a recipe that generates optimal statistical procedures (analogues of the MLE) in the new settings, showing how to achieve the new Fisher information lower bounds.
| Author | : Denis Belomestny |
| Publisher | : Springer Nature |
| Total Pages | : 603 |
| Release | : 2023-07-16 |
| Genre | : Mathematics |
| ISBN | : 3031301145 |
Download Foundations of Modern Statistics Book in PDF, ePub and Kindle
This book contains contributions from the participants of the international conference “Foundations of Modern Statistics” which took place at Weierstrass Institute for Applied Analysis and Stochastics (WIAS), Berlin, during November 6–8, 2019, and at Higher School of Economics (HSE University), Moscow, during November 30, 2019. The events were organized in honor of Professor Vladimir Spokoiny on the occasion of his 60th birthday. Vladimir Spokoiny has pioneered the field of adaptive statistical inference and contributed to a variety of its applications. His more than 30 years of research in the field of mathematical statistics had a great influence on the development of the mathematical theory of statistics to its present state. It has inspired many young researchers to start their research in this exciting field of mathematics. The papers contained in this book reflect the broad field of interests of Vladimir Spokoiny: optimal rates and non-asymptotic bounds in nonparametrics, Bayes approaches from a frequentist point of view, optimization, signal processing, and statistical theory motivated by models in applied fields. Materials prepared by famous scientists contain original scientific results, which makes the publication valuable for researchers working in these fields. The book concludes by a conversation of Vladimir Spokoiny with Markus Reiβ and Enno Mammen. This interview gives some background on the life of Vladimir Spokoiny and his many scientific interests and motivations.
| Author | : Ding-Zhu Du |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 300 |
| Release | : 2013-12-01 |
| Genre | : Computers |
| ISBN | : 1461335574 |
Download Minimax and Applications Book in PDF, ePub and Kindle
Techniques and principles of minimax theory play a key role in many areas of research, including game theory, optimization, and computational complexity. In general, a minimax problem can be formulated as min max f(x, y) (1) ",EX !lEY where f(x, y) is a function defined on the product of X and Y spaces. There are two basic issues regarding minimax problems: The first issue concerns the establishment of sufficient and necessary conditions for equality minmaxf(x,y) = maxminf(x,y). (2) "'EX !lEY !lEY "'EX The classical minimax theorem of von Neumann is a result of this type. Duality theory in linear and convex quadratic programming interprets minimax theory in a different way. The second issue concerns the establishment of sufficient and necessary conditions for values of the variables x and y that achieve the global minimax function value f(x*, y*) = minmaxf(x, y). (3) "'EX !lEY There are two developments in minimax theory that we would like to mention.
| Author | : Sam Efromovich |
| Publisher | : CRC Press |
| Total Pages | : 448 |
| Release | : 2018-03-12 |
| Genre | : Mathematics |
| ISBN | : 1351679848 |
Download Missing and Modified Data in Nonparametric Estimation Book in PDF, ePub and Kindle
This book presents a systematic and unified approach for modern nonparametric treatment of missing and modified data via examples of density and hazard rate estimation, nonparametric regression, filtering signals, and time series analysis. All basic types of missing at random and not at random, biasing, truncation, censoring, and measurement errors are discussed, and their treatment is explained. Ten chapters of the book cover basic cases of direct data, biased data, nondestructive and destructive missing, survival data modified by truncation and censoring, missing survival data, stationary and nonstationary time series and processes, and ill-posed modifications. The coverage is suitable for self-study or a one-semester course for graduate students with a prerequisite of a standard course in introductory probability. Exercises of various levels of difficulty will be helpful for the instructor and self-study. The book is primarily about practically important small samples. It explains when consistent estimation is possible, and why in some cases missing data should be ignored and why others must be considered. If missing or data modification makes consistent estimation impossible, then the author explains what type of action is needed to restore the lost information. The book contains more than a hundred figures with simulated data that explain virtually every setting, claim, and development. The companion R software package allows the reader to verify, reproduce and modify every simulation and used estimators. This makes the material fully transparent and allows one to study it interactively. Sam Efromovich is the Endowed Professor of Mathematical Sciences and the Head of the Actuarial Program at the University of Texas at Dallas. He is well known for his work on the theory and application of nonparametric curve estimation and is the author of Nonparametric Curve Estimation: Methods, Theory, and Applications. Professor Sam Efromovich is a Fellow of the Institute of Mathematical Statistics and the American Statistical Association.
| Author | : |
| Publisher | : |
| Total Pages | : 730 |
| Release | : 1966 |
| Genre | : Mathematics |
| ISBN | : |
Download Mathematica Scandinavica Book in PDF, ePub and Kindle
| Author | : |
| Publisher | : |
| Total Pages | : 812 |
| Release | : 1997 |
| Genre | : Mathematical statistics |
| ISBN | : |
Download Current Index to Statistics, Applications, Methods and Theory Book in PDF, ePub and Kindle
The Current Index to Statistics (CIS) is a bibliographic index of publications in statistics, probability, and related fields.
| Author | : Behrouz Farhang-Boroujeny |
| Publisher | : John Wiley & Sons |
| Total Pages | : 800 |
| Release | : 2013-04-02 |
| Genre | : Technology & Engineering |
| ISBN | : 111859133X |
Download Adaptive Filters Book in PDF, ePub and Kindle
This second edition of Adaptive Filters: Theory and Applications has been updated throughout to reflect the latest developments in this field; notably an increased coverage given to the practical applications of the theory to illustrate the much broader range of adaptive filters applications developed in recent years. The book offers an easy to understand approach to the theory and application of adaptive filters by clearly illustrating how the theory explained in the early chapters of the book is modified for the various applications discussed in detail in later chapters. This integrated approach makes the book a valuable resource for graduate students; and the inclusion of more advanced applications including antenna arrays and wireless communications makes it a suitable technical reference for engineers, practitioners and researchers. Key features: • Offers a thorough treatment of the theory of adaptive signal processing; incorporating new material on transform domain, frequency domain, subband adaptive filters, acoustic echo cancellation and active noise control. • Provides an in-depth study of applications which now includes extensive coverage of OFDM, MIMO and smart antennas. • Contains exercises and computer simulation problems at the end of each chapter. • Includes a new companion website hosting MATLAB® simulation programs which complement the theoretical analyses, enabling the reader to gain an in-depth understanding of the behaviours and properties of the various adaptive algorithms.
| Author | : David G. Luenberger |
| Publisher | : John Wiley & Sons |
| Total Pages | : 348 |
| Release | : 1997-01-23 |
| Genre | : Technology & Engineering |
| ISBN | : 9780471181170 |
Download Optimization by Vector Space Methods Book in PDF, ePub and Kindle
Engineers must make decisions regarding the distribution of expensive resources in a manner that will be economically beneficial. This problem can be realistically formulated and logically analyzed with optimization theory. This book shows engineers how to use optimization theory to solve complex problems. Unifies the large field of optimization with a few geometric principles. Covers functional analysis with a minimum of mathematics. Contains problems that relate to the applications in the book.
| Author | : Sam Efromovich |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 423 |
| Release | : 2008-01-19 |
| Genre | : Mathematics |
| ISBN | : 0387226389 |
Download Nonparametric Curve Estimation Book in PDF, ePub and Kindle
This book gives a systematic, comprehensive, and unified account of modern nonparametric statistics of density estimation, nonparametric regression, filtering signals, and time series analysis. The companion software package, available over the Internet, brings all of the discussed topics into the realm of interactive research. Virtually every claim and development mentioned in the book is illustrated with graphs which are available for the reader to reproduce and modify, making the material fully transparent and allowing for complete interactivity.
| Author | : Evarist Giné |
| Publisher | : Cambridge University Press |
| Total Pages | : 706 |
| Release | : 2021-03-25 |
| Genre | : Mathematics |
| ISBN | : 1009022784 |
Download Mathematical Foundations of Infinite-Dimensional Statistical Models Book in PDF, ePub and Kindle
In nonparametric and high-dimensional statistical models, the classical Gauss–Fisher–Le Cam theory of the optimality of maximum likelihood estimators and Bayesian posterior inference does not apply, and new foundations and ideas have been developed in the past several decades. This book gives a coherent account of the statistical theory in infinite-dimensional parameter spaces. The mathematical foundations include self-contained 'mini-courses' on the theory of Gaussian and empirical processes, approximation and wavelet theory, and the basic theory of function spaces. The theory of statistical inference in such models - hypothesis testing, estimation and confidence sets - is presented within the minimax paradigm of decision theory. This includes the basic theory of convolution kernel and projection estimation, but also Bayesian nonparametrics and nonparametric maximum likelihood estimation. In a final chapter the theory of adaptive inference in nonparametric models is developed, including Lepski's method, wavelet thresholding, and adaptive inference for self-similar functions. Winner of the 2017 PROSE Award for Mathematics.
