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Author: Wayne Yuan Gao
Publisher:
ISBN:
Category :
Languages : en
Pages : 16
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Book Description
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.
Author: Wayne Yuan Gao
Publisher:
ISBN:
Category :
Languages : en
Pages : 16
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Book Description
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.
Author: A.P. Korostelev
Publisher: Springer Science & Business Media
ISBN: 1461227127
Category : Mathematics
Languages : en
Pages : 272
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Book Description
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.
Author: Oleksandr Nakonechnyi
Publisher: CRC Press
ISBN: 1000795136
Category : Mathematics
Languages : en
Pages : 233
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Book Description
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.
Author: Jianqing Fan
Publisher: Routledge
ISBN: 1351434810
Category : Mathematics
Languages : en
Pages : 358
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Book Description
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.
Author: Erich L. Lehmann
Publisher: Springer Science & Business Media
ISBN: 0387227288
Category : Mathematics
Languages : en
Pages : 610
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Book Description
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".
Author: Richard Farebrother
Publisher: Springer Science & Business Media
ISBN: 3642363008
Category : Mathematics
Languages : en
Pages : 59
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Book Description
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.
Author: Milton Bernard Adams
Publisher:
ISBN:
Category : Stochastic processes
Languages : en
Pages : 16
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Book Description
Author: Jürgen Pilz
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 316
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Book Description
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.
Author: Soebanar
Publisher:
ISBN:
Category :
Languages : en
Pages : 232
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Book Description
Author: Markus Frölich
Publisher: Springer Science & Business Media
ISBN: 3642557163
Category : Business & Economics
Languages : en
Pages : 194
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Book Description
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.
