The Theory Of Linear Prediction
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| Author | : P. Vaidyanathan |
| Publisher | : Springer Nature |
| Total Pages | : 183 |
| Release | : 2022-06-01 |
| Genre | : Technology & Engineering |
| ISBN | : 303102527X |
Linear prediction theory has had a profound impact in the field of digital signal processing. Although the theory dates back to the early 1940s, its influence can still be seen in applications today. The theory is based on very elegant mathematics and leads to many beautiful insights into statistical signal processing. Although prediction is only a part of the more general topics of linear estimation, filtering, and smoothing, this book focuses on linear prediction. This has enabled detailed discussion of a number of issues that are normally not found in texts. For example, the theory of vector linear prediction is explained in considerable detail and so is the theory of line spectral processes. This focus and its small size make the book different from many excellent texts which cover the topic, including a few that are actually dedicated to linear prediction. There are several examples and computer-based demonstrations of the theory. Applications are mentioned wherever appropriate, but the focus is not on the detailed development of these applications. The writing style is meant to be suitable for self-study as well as for classroom use at the senior and first-year graduate levels. The text is self-contained for readers with introductory exposure to signal processing, random processes, and the theory of matrices, and a historical perspective and detailed outline are given in the first chapter. Table of Contents: Introduction / The Optimal Linear Prediction Problem / Levinson's Recursion / Lattice Structures for Linear Prediction / Autoregressive Modeling / Prediction Error Bound and Spectral Flatness / Line Spectral Processes / Linear Prediction Theory for Vector Processes / Appendix A: Linear Estimation of Random Variables / B: Proof of a Property of Autocorrelations / C: Stability of the Inverse Filter / Recursion Satisfied by AR Autocorrelations
| Author | : Peter Strobach |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 434 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 3642752063 |
Lnear prediction theory and the related algorithms have matured to the point where they now form an integral part of many real-world adaptive systems. When it is necessary to extract information from a random process, we are frequently faced with the problem of analyzing and solving special systems of linear equations. In the general case these systems are overdetermined and may be characterized by additional properties, such as update and shift-invariance properties. Usually, one employs exact or approximate least-squares methods to solve the resulting class of linear equations. Mainly during the last decade, researchers in various fields have contributed techniques and nomenclature for this type of least-squares problem. This body of methods now constitutes what we call the theory of linear prediction. The immense interest that it has aroused clearly emerges from recent advances in processor technology, which provide the means to implement linear prediction algorithms, and to operate them in real time. The practical effect is the occurrence of a new class of high-performance adaptive systems for control, communications and system identification applications. This monograph presumes a background in discrete-time digital signal processing, including Z-transforms, and a basic knowledge of discrete-time random processes. One of the difficulties I have en countered while writing this book is that many engineers and computer scientists lack knowledge of fundamental mathematics and geometry.
| Author | : P. P. Vaidyanathan |
| Publisher | : Morgan & Claypool Publishers |
| Total Pages | : 198 |
| Release | : 2008 |
| Genre | : Prediction theory |
| ISBN | : 1598295756 |
Of Properties Relating to Levinson's Recursion.
| Author | : J.D. Markel |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 276 |
| Release | : 2013-03-12 |
| Genre | : Science |
| ISBN | : 3642662862 |
During the past ten years a new area in speech processing, generally referred to as linear prediction, has evolved. As with all scientific research, results did not always get published in a logical order and terminology was not always con sistent. In mid-1974, we decided to begin an extra hours and weekends project of organizing the literature in linear prediction of speech and developing it into a unified presentation in terms of content and terminology. This effort was completed in November, 1975, with the contents presented herein. If there are two words which describe our goals in this book, they are unifica tion and depth. Considerable effort has been spent on showing the interrelation ships among various linear prediction formulations and solutions, and in develop ing extensions such as acoustic tube models and synthesis filter structures in a unified manner with consistent terminology. Topics are presented in such a manner that derivations and theoretical details are covered, along with Fortran sub routines and practical considerations. Using this approach we hope to have made the material useful for a wide range of backgrounds and interests.
| Author | : Christoph Molnar |
| Publisher | : Lulu.com |
| Total Pages | : 320 |
| Release | : 2020 |
| Genre | : Artificial intelligence |
| ISBN | : 0244768528 |
This book is about making machine learning models and their decisions interpretable. After exploring the concepts of interpretability, you will learn about simple, interpretable models such as decision trees, decision rules and linear regression. Later chapters focus on general model-agnostic methods for interpreting black box models like feature importance and accumulated local effects and explaining individual predictions with Shapley values and LIME. All interpretation methods are explained in depth and discussed critically. How do they work under the hood? What are their strengths and weaknesses? How can their outputs be interpreted? This book will enable you to select and correctly apply the interpretation method that is most suitable for your machine learning project.
| Author | : Dale L. Zimmerman |
| Publisher | : Springer Nature |
| Total Pages | : 504 |
| Release | : 2020-11-02 |
| Genre | : Mathematics |
| ISBN | : 3030520633 |
This textbook presents a unified and rigorous approach to best linear unbiased estimation and prediction of parameters and random quantities in linear models, as well as other theory upon which much of the statistical methodology associated with linear models is based. The single most unique feature of the book is that each major concept or result is illustrated with one or more concrete examples or special cases. Commonly used methodologies based on the theory are presented in methodological interludes scattered throughout the book, along with a wealth of exercises that will benefit students and instructors alike. Generalized inverses are used throughout, so that the model matrix and various other matrices are not required to have full rank. Considerably more emphasis is given to estimability, partitioned analyses of variance, constrained least squares, effects of model misspecification, and most especially prediction than in many other textbooks on linear models. This book is intended for master and PhD students with a basic grasp of statistical theory, matrix algebra and applied regression analysis, and for instructors of linear models courses. Solutions to the book’s exercises are available in the companion volume Linear Model Theory - Exercises and Solutions by the same author.
| Author | : Alvin C. Rencher |
| Publisher | : John Wiley & Sons |
| Total Pages | : 690 |
| Release | : 2008-01-07 |
| Genre | : Mathematics |
| ISBN | : 0470192607 |
The essential introduction to the theory and application of linear models—now in a valuable new edition Since most advanced statistical tools are generalizations of the linear model, it is neces-sary to first master the linear model in order to move forward to more advanced concepts. The linear model remains the main tool of the applied statistician and is central to the training of any statistician regardless of whether the focus is applied or theoretical. This completely revised and updated new edition successfully develops the basic theory of linear models for regression, analysis of variance, analysis of covariance, and linear mixed models. Recent advances in the methodology related to linear mixed models, generalized linear models, and the Bayesian linear model are also addressed. Linear Models in Statistics, Second Edition includes full coverage of advanced topics, such as mixed and generalized linear models, Bayesian linear models, two-way models with empty cells, geometry of least squares, vector-matrix calculus, simultaneous inference, and logistic and nonlinear regression. Algebraic, geometrical, frequentist, and Bayesian approaches to both the inference of linear models and the analysis of variance are also illustrated. Through the expansion of relevant material and the inclusion of the latest technological developments in the field, this book provides readers with the theoretical foundation to correctly interpret computer software output as well as effectively use, customize, and understand linear models. This modern Second Edition features: New chapters on Bayesian linear models as well as random and mixed linear models Expanded discussion of two-way models with empty cells Additional sections on the geometry of least squares Updated coverage of simultaneous inference The book is complemented with easy-to-read proofs, real data sets, and an extensive bibliography. A thorough review of the requisite matrix algebra has been addedfor transitional purposes, and numerous theoretical and applied problems have been incorporated with selected answers provided at the end of the book. A related Web site includes additional data sets and SAS® code for all numerical examples. Linear Model in Statistics, Second Edition is a must-have book for courses in statistics, biostatistics, and mathematics at the upper-undergraduate and graduate levels. It is also an invaluable reference for researchers who need to gain a better understanding of regression and analysis of variance.
| Author | : Peter Whittle |
| Publisher | : |
| Total Pages | : 187 |
| Release | : 1983 |
| Genre | : Mathematics |
| ISBN | : 9780816611485 |
Prediction and Regulation by Linear Least-Square Methods was first published in 1963. This revised second edition was issued in 1983. Minnesota Archive Editions uses digital technology to make long-unavailable books once again accessible, and are published unaltered from the original University of Minnesota Press editions.During the past two decades, statistical theories of prediction and control have assumed an increasing importance in all fields of scientific research. To understand a phenomenon is to be able to predict it and to influence it in predictable ways. First published in 1963 and long out of print, Prediction and Regulation by Linear Least-Square Methods offers important tools for constructing models of dynamic phenomena. This elegantly written book has been a basic reference for researchers in many applied sciences who seek practical information about the representation and manipulation of stationary stochastic processes. Peter Whittle’s text has a devoted group of readers and users, especially among economists. This edition contains the unchanged text of the original and adds new works by the author and a foreword by economist Thomas J. Sargent.
| Author | : Ronald Christensen |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 480 |
| Release | : 1996 |
| Genre | : Mathematics |
| ISBN | : |
This textbook provides a wide-ranging introduction to the use of linear models in analyzing data. The author's emphasis is on providing a unified treatment of the analysis of variance models and regression models by presenting a vector space and projections approach to the subject. Every chapter comes with numerous exercises and examples, which will make it ideal for a graduate-level course on this subject.
| Author | : Xin Yan |
| Publisher | : World Scientific |
| Total Pages | : 349 |
| Release | : 2009 |
| Genre | : Mathematics |
| ISBN | : 9812834109 |
"This volume presents in detail the fundamental theories of linear regression analysis and diagnosis, as well as the relevant statistical computing techniques so that readers are able to actually model the data using the techniques described in the book. This book is suitable for graduate students who are either majoring in statistics/biostatistics or using linear regression analysis substantially in their subject area." --Book Jacket.
