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Author: STANFORD UNIV CALIF DEPT OF STATISTICS. Publisher: ISBN: Category : Languages : en Pages : 8
Book Description
The problem of estimating the bounds of random variables has been previously discussed. Here we discuss optimality of estimates when the data is censored so that only the r largest or smallest of the observations is available for estimating a bound. For fixed r we find the linear function of the censored data which is the optimal estimator of a bound in the sense that, when the sample size is large, the estimator has smallest mean squared error among all such linear estimators. Provided r is not close to one, these estimators are almost optimal when the entire sample is available since, for example, when estimating an upper bound and the sample size is large, the largest few observations carry most of the information about the bound. This fact is illustrated in one case.
Author: STANFORD UNIV CALIF DEPT OF STATISTICS. Publisher: ISBN: Category : Languages : en Pages : 8
Book Description
The problem of estimating the bounds of random variables has been previously discussed. Here we discuss optimality of estimates when the data is censored so that only the r largest or smallest of the observations is available for estimating a bound. For fixed r we find the linear function of the censored data which is the optimal estimator of a bound in the sense that, when the sample size is large, the estimator has smallest mean squared error among all such linear estimators. Provided r is not close to one, these estimators are almost optimal when the entire sample is available since, for example, when estimating an upper bound and the sample size is large, the largest few observations carry most of the information about the bound. This fact is illustrated in one case.
Author: Anatoly Zhigljavsky Publisher: Springer Science & Business Media ISBN: 0387747400 Category : Mathematics Languages : en Pages : 269
Book Description
This book examines the main methodological and theoretical developments in stochastic global optimization. It is designed to inspire readers to explore various stochastic methods of global optimization by clearly explaining the main methodological principles and features of the methods. Among the book’s features is a comprehensive study of probabilistic and statistical models underlying the stochastic optimization algorithms.
Author: Aimo Törn Publisher: Springer Science & Business Media ISBN: 0387367217 Category : Mathematics Languages : en Pages : 362
Book Description
The research of Antanas Zilinskas has focused on developing models for global optimization, implementing and investigating the corresponding algorithms, and applying those algorithms to practical problems. This volume, dedicated to Professor Zilinskas on the occasion of his 60th birthday, contains new survey papers in which leading researchers from the field present various models and algorithms for solving global optimization problems.
Author: Jagdish S. Rustagi Publisher: Academic Press ISBN: 1483260348 Category : Mathematics Languages : en Pages : 505
Book Description
Optimizing Method in Statistics is a compendium of papers dealing with variational methods, regression analysis, mathematical programming, optimum seeking methods, stochastic control, optimum design of experiments, optimum spacings, and order statistics. One paper reviews three optimization problems encountered in parameter estimation, namely, 1) iterative procedures for maximum likelihood estimation, based on complete or censored samples, of the parameters of various populations; 2) optimum spacings of quantiles for linear estimation; and 3) optimum choice of order statistics for linear estimation. Another paper notes the possibility of posing various adaptive filter algorithms to make the filter learn the system model while the system is operating in real time. By reducing the time necessary for process modeling, the time required to implement the acceptable system design can also be reduced One paper evaluates the parallel structure between duality relationships for the linear functional version of the generalized Neyman-Pearson problem, as well as the duality relationships of linear programming as these apply to bounded-variable linear programming problems. The compendium can prove beneficial to mathematicians, students, and professor of calculus, statistics, or advanced mathematics.
Author: P. P. Vaidyanathan Publisher: Morgan & Claypool Publishers ISBN: 1598295764 Category : Technology & Engineering Languages : en Pages : 198
Book Description
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: Javier Rojo Publisher: IMS ISBN: 9780940600652 Category : Estimation theory Languages : en Pages : 366
Book Description
The volume presents a collection of refereed papers dealing with the issue of optimality in several areas including: multiple testing, transformation models, competing risks, regression trees, density estimation, copulas, and robustness.
Author: STANFORD UNIV CALIF DEPT OF STATISTICS.
Author: STANFORD UNIV CALIF DEPT OF STATISTICS.
Author: 
Author: Anatoly Zhigljavsky
Author: 
Author: Aimo Törn
Author: Beong-Soo So
Author: Roman Vershynin
Author: Jagdish S. Rustagi
Author: P. P. Vaidyanathan
Author: Javier Rojo