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Minimax Linear Estimation At A Boundary Point
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Book Synopsis Minimax Linear Estimation at a Boundary Point by : Wayne Yuan Gao
Download or read book Minimax Linear Estimation at a Boundary Point written by Wayne Yuan Gao and published by . This book was released on 2017 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper characterizes the minimax linear estimator of the value of an unknown function at a boundary point of its domain in a Gaussian white noise model under the restriction that the first-order derivative of the unknown function is Lipschitz continuous (the second-order Holder class). The result is then applied to construct the minimax optimal estimator for the regression discontinuity design model, where the parameter of interest involves function values at boundary points.
Book Synopsis Minimax Theory of Image Reconstruction by : A.P. Korostelev
Download or read book Minimax Theory of Image Reconstruction written by A.P. Korostelev and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: There exists a large variety of image reconstruction methods proposed by different authors (see e. g. Pratt (1978), Rosenfeld and Kak (1982), Marr (1982)). Selection of an appropriate method for a specific problem in image analysis has been always considered as an art. How to find the image reconstruction method which is optimal in some sense? In this book we give an answer to this question using the asymptotic minimax approach in the spirit of Ibragimov and Khasminskii (1980a,b, 1981, 1982), Bretagnolle and Huber (1979), Stone (1980, 1982). We assume that the image belongs to a certain functional class and we find the image estimators that achieve the best order of accuracy for the worst images in the class. This concept of optimality is rather rough since only the order of accuracy is optimized. However, it is useful for comparing various image reconstruction methods. For example, we show that some popular methods such as simple linewise processing and linear estimation are not optimal for images with sharp edges. Note that discontinuity of images is an important specific feature appearing in most practical situations where one has to distinguish between the "image domain" and the "background" . The approach of this book is based on generalization of nonparametric regression and nonparametric change-point techniques. We discuss these two basic problems in Chapter 1. Chapter 2 is devoted to minimax lower bounds for arbitrary estimators in general statistical models.
Book Synopsis Guaranteed Estimation Problems in the Theory of Linear Ordinary Differential Equations with Uncertain Data by : Oleksandr Nakonechnyi
Download or read book Guaranteed Estimation Problems in the Theory of Linear Ordinary Differential Equations with Uncertain Data written by Oleksandr Nakonechnyi and published by CRC Press. This book was released on 2022-09-01 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to the construction of optimal estimates of values of linear functionals on solutions to Cauchy and two-point boundary value problems for systems of linear first-order ordinary differential equations, from indirect observations which are linear transformations of the same solutions perturbed by additive random noises. It is assumed that right-hand sides of equations and boundary data as well as statistical characteristics of random noises in observations are not known and belong to certain given sets in corresponding functional spaces. This leads to the necessity of introducing the minimax statement of an estimation problem when optimal estimates are defined as linear, with respect to observations, estimates for which the maximum of mean square error of estimation taken over the above-mentioned sets attains minimal value. Such estimates are called minimax or guaranteed estimates. It is established that these estimates are expressed explicitly via solutions to some uniquely solvable linear systems of ordinary differential equations of the special type. The authors apply these results for obtaining the optimal estimates of solutions from indirect noisy observations. Similar estimation problems for solutions of boundary value problems for linear differential equations of order n with general boundary conditions are considered. The authors also elaborate guaranteed estimation methods under incomplete data of unknown right-hand sides of equations and boundary data and obtain representations for the corresponding guaranteed estimates. In all the cases estimation errors are determined.
Book Synopsis Local Polynomial Modelling and Its Applications by : Jianqing Fan
Download or read book Local Polynomial Modelling and Its Applications written by Jianqing Fan and published by Routledge. This book was released on 2018-05-02 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: Data-analytic approaches to regression problems, arising from many scientific disciplines are described in this book. The aim of these nonparametric methods is to relax assumptions on the form of a regression function and to let data search for a suitable function that describes the data well. The use of these nonparametric functions with parametric techniques can yield very powerful data analysis tools. Local polynomial modeling and its applications provides an up-to-date picture on state-of-the-art nonparametric regression techniques. The emphasis of the book is on methodologies rather than on theory, with a particular focus on applications of nonparametric techniques to various statistical problems. High-dimensional data-analytic tools are presented, and the book includes a variety of examples. This will be a valuable reference for research and applied statisticians, and will serve as a textbook for graduate students and others interested in nonparametric regression.
Book Synopsis Theory of Point Estimation by : Erich L. Lehmann
Download or read book Theory of Point Estimation written by Erich L. Lehmann and published by Springer Science & Business Media. This book was released on 2006-05-02 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second, much enlarged edition by Lehmann and Casella of Lehmann's classic text on point estimation maintains the outlook and general style of the first edition. All of the topics are updated, while an entirely new chapter on Bayesian and hierarchical Bayesian approaches is provided, and there is much new material on simultaneous estimation. Each chapter concludes with a Notes section which contains suggestions for further study. This is a companion volume to the second edition of Lehmann's "Testing Statistical Hypotheses".
Book Synopsis L1-Norm and L∞-Norm Estimation by : Richard Farebrother
Download or read book L1-Norm and L∞-Norm Estimation written by Richard Farebrother and published by Springer Science & Business Media. This book was released on 2013-04-03 with total page 59 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is concerned with the fitting of linear relationships in the context of the linear statistical model. As alternatives to the familiar least squared residuals procedure, it investigates the relationships between the least absolute residuals, the minimax absolute residual and the least median of squared residuals procedures. It is intended for graduate students and research workers in statistics with some command of matrix analysis and linear programming techniques.
Book Synopsis Bayesian Estimation and Experimental Design in Linear Regression Models by : Jürgen Pilz
Download or read book Bayesian Estimation and Experimental Design in Linear Regression Models written by Jürgen Pilz and published by . This book was released on 1991-07-09 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a clear treatment of the design and analysis of linear regression experiments in the presence of prior knowledge about the model parameters. Develops a unified approach to estimation and design; provides a Bayesian alternative to the least squares estimator; and indicates methods for the construction of optimal designs for the Bayes estimator. Material is also applicable to some well-known estimators using prior knowledge that is not available in the form of a prior distribution for the model parameters; such as mixed linear, minimax linear and ridge-type estimators.
Book Synopsis Linear Estimation of Two-point Boundary Value Processes by : Milton Bernard Adams
Download or read book Linear Estimation of Two-point Boundary Value Processes written by Milton Bernard Adams and published by . This book was released on 1983 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Minimax Estimation with Respect to Restricted Parameter Sets by : Soebanar
Download or read book Minimax Estimation with Respect to Restricted Parameter Sets written by Soebanar and published by . This book was released on 1987 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Programme Evaluation and Treatment Choice by : Markus Frölich
Download or read book Programme Evaluation and Treatment Choice written by Markus Frölich and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: Policy evaluation and programme choice are important tools for informed decision-making, for the administration of active labour market programmes, training programmes, tuition subsidies, rehabilitation programmes etc. Whereas the evaluation of programmes and policies is mainly concerned with an overall assessment of impact, benefits and costs, programme choice considers an optimal allocation of individuals to the programmes. This book surveys potential evaluation strategies for policies with multiple programmes and discusses evaluation and treatment choice in a coherent framework. Recommendations for choosing appropriate evaluation estimators are derived. Furthermore, a semiparametric estimator of optimal treatment choice is developed to assist in the optimal allocation of participants.
Book Synopsis Nonparametric Statistical Methods And Related Topics: A Festschrift In Honor Of Professor P K Bhattacharya On The Occasion Of His 80th Birthday by : Francisco J Samaniego
Download or read book Nonparametric Statistical Methods And Related Topics: A Festschrift In Honor Of Professor P K Bhattacharya On The Occasion Of His 80th Birthday written by Francisco J Samaniego and published by World Scientific. This book was released on 2011-09-16 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of 22 research papers by leading researchers in Probability and Statistics. Many of the papers are focused on themes that Professor Bhattacharya has published on research. Topics of special interest include nonparametric inference, nonparametric curve fitting, linear model theory, Bayesian nonparametrics, change point problems, time series analysis and asymptotic theory.This volume presents state-of-the-art research in statistical theory, with an emphasis on nonparametric inference, linear model theory, time series analysis and asymptotic theory. It will serve as a valuable reference to the statistics research community as well as to practitioners who utilize methodology in these areas of emphasis.
Book Synopsis Minimax Estimation in Regression and Random Censorship Models by : Eduard N. Belitser
Download or read book Minimax Estimation in Regression and Random Censorship Models written by Eduard N. Belitser and published by . This book was released on 2000 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Minimax Under Transportation Constrains by : Vladimir Tsurkov
Download or read book Minimax Under Transportation Constrains written by Vladimir Tsurkov and published by Springer Science & Business Media. This book was released on 1999-04-30 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Transportation problems belong to the domains mathematical program ming and operations research. Transportation models are widely applied in various fields. Numerous concrete problems (for example, assignment and distribution problems, maximum-flow problem, etc. ) are formulated as trans portation problems. Some efficient methods have been developed for solving transportation problems of various types. This monograph is devoted to transportation problems with minimax cri teria. The classical (linear) transportation problem was posed several decades ago. In this problem, supply and demand points are given, and it is required to minimize the transportation cost. This statement paved the way for numerous extensions and generalizations. In contrast to the original statement of the problem, we consider a min imax rather than a minimum criterion. In particular, a matrix with the minimal largest element is sought in the class of nonnegative matrices with given sums of row and column elements. In this case, the idea behind the minimax criterion can be interpreted as follows. Suppose that the shipment time from a supply point to a demand point is proportional to the amount to be shipped. Then, the minimax is the minimal time required to transport the total amount. It is a common situation that the decision maker does not know the tariff coefficients. In other situations, they do not have any meaning at all, and neither do nonlinear tariff objective functions. In such cases, the minimax interpretation leads to an effective solution.
Book Synopsis Minimax Estimation by : Workshop on Linear Minimax Estimation - Theory and Practice
Download or read book Minimax Estimation written by Workshop on Linear Minimax Estimation - Theory and Practice and published by . This book was released on 1996 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis An Application of a Linear Programming Technique to Nonlinear Minimax Problems by : James R. Schiess
Download or read book An Application of a Linear Programming Technique to Nonlinear Minimax Problems written by James R. Schiess and published by . This book was released on 1973 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: A differential correction technique for solving nonlinear minimax problems is presented. The basis of the technique is a linear programing algorithm which solves the linear minimax problem. By linearizing the original nonlinear equations about a nominal solution, both nonlinear approximation and estimation problems using the minimax norm may be solved iteratively. Some consideration is also given to improving convergence and to the treatment of problems with more than one measured quantity. A sample problem is treated with this technique and with the least-squares differential correction method to illustrate the properties of the minimax solution. The results indicate that for the sample approximation problem, the minimax technique provides better estimates than the least-squares method if a sufficient amount of data is used. For the sample estimation problem, the minimax estimates are better if the mathematical model is incomplete.
Book Synopsis Minimax Estimation of Non-random Signals by : Randall K. Bahr
Download or read book Minimax Estimation of Non-random Signals written by Randall K. Bahr and published by . This book was released on 1986 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Statistical Methods of Model Building: Nonlinear regression, functional relations, and robust methods by : Helga Bunke
Download or read book Statistical Methods of Model Building: Nonlinear regression, functional relations, and robust methods written by Helga Bunke and published by . This book was released on 1986 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt:
