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Quasi Minimax Estimation In The Linear Regression Model
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Book Synopsis Quasi minimax estimation in the linear regression model by : Peter Stahlecker
Download or read book Quasi minimax estimation in the linear regression model written by Peter Stahlecker and published by . This book was released on 1984 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis On minimax estimation in linear regression models with ellipsoidal constraints by : Norbert Christopeit
Download or read book On minimax estimation in linear regression models with ellipsoidal constraints written by Norbert Christopeit and published by . This book was released on 1991 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Linear Regression written by Jürgen Groß and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book covers the basic theory of linear regression models and presents a comprehensive survey of different estimation techniques as alternatives and complements to least squares estimation. Proofs are given for the most relevant results, and the presented methods are illustrated with the help of numerical examples and graphics. Special emphasis is placed on practicability and possible applications. The book is rounded off by an introduction to the basics of decision theory and an appendix on matrix algebra.
Book Synopsis Minimax Estimation in the Linear Regression Model with Fuzzy Inequality Constraints by : Henning Knautz
Download or read book Minimax Estimation in the Linear Regression Model with Fuzzy Inequality Constraints written by Henning Knautz and published by . This book was released on 2000 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Minimax Estimation in Linear Regression Under Restrictions by : Helge Blaker
Download or read book Minimax Estimation in Linear Regression Under Restrictions written by Helge Blaker and published by . This book was released on 1998 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis ˜Aœ Note on Minimax Estimation in Linear Regression by : Karsten Schmidt
Download or read book ˜Aœ Note on Minimax Estimation in Linear Regression written by Karsten Schmidt and published by . This book was released on 1991 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Multiple Testing and Minimax Estimation in Sparse Linear Regression by : Weijie Su
Download or read book Multiple Testing and Minimax Estimation in Sparse Linear Regression written by Weijie Su and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In many real-world statistical problems, we observe a response variable of interest together with a large number of potentially explanatory variables of which a majority may be irrelevant. For this type of problem, controlling the false discovery rate (FDR) guarantees that most of the selected variables, often termed discoveries in a scientific context, are truly explanatory and thus replicable. Inspired by ideas from the Benjamini-Hochberg procedure (BHq), this thesis proposes a new method named SLOPE to control the FDR in sparse high-dimensional linear regression. SLOPE is a computationally efficient procedure that works by regularizing the fitted coefficients according to their ranks: the higher the rank, the larger the penalty. This adaptive regularization is analogous to the BHq, which compares more significant p-values with more stringent thresholds. Under orthogonal designs, SLOPE with the BHq critical values is proven to control FDR at any given level. Moreover, we demonstrate empirically that this method also appears to have appreciable inferential properties under more general design matrices while offering substantial power. The thesis proceeds to explore the estimation properties of SLOPE. Although SLOPE was developed from a multiple testing viewpoint, we show the surprising result that it achieves optimal squared errors under Gaussian random designs. This optimality holds under a weak assumption on the l0-sparsity level of the underlying signals, and is sharp in the sense that this is the best possible error any estimator can achieve. An appealing feature is that SLOPE does not require any knowledge of the degree of sparsity, and yet automatically adapts to yield optimal total squared errors over a wide range of l0-sparsity classes. Finally, we conclude this thesis by focusing on Nesterov's accelerated scheme, which is integral to a fast algorithmic implementation of SLOPE. Specifically, we prove that, as the step size vanishes, this scheme converges in a rigorous sense to a second-order ordinary differential equation (ODE). This continuous time ODE allows for a better understanding of Nesterov's scheme, and thus it can serve as a tool for analyzing and generalizing this scheme. A fruitful application of this tool yields a family of schemes with similar convergence rates. The ODE interpretation also suggests restarting Nesterov's scheme leading to a new algorithm, which is proven to converge at a linear rate whenever the objective is strongly convex.
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 estimation in linear regression with convex polyhedral constraints by : Peter Stahlecker
Download or read book Minimax estimation in linear regression with convex polyhedral constraints written by Peter Stahlecker and published by . This book was released on 1990 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Quasi-Least Squares Regression by : Justine Shults
Download or read book Quasi-Least Squares Regression written by Justine Shults and published by CRC Press. This book was released on 2014-01-28 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: Drawing on the authors’ substantial expertise in modeling longitudinal and clustered data, Quasi-Least Squares Regression provides a thorough treatment of quasi-least squares (QLS) regression—a computational approach for the estimation of correlation parameters within the framework of generalized estimating equations (GEEs). The authors present a detailed evaluation of QLS methodology, demonstrating the advantages of QLS in comparison with alternative methods. They describe how QLS can be used to extend the application of the traditional GEE approach to the analysis of unequally spaced longitudinal data, familial data, and data with multiple sources of correlation. In some settings, QLS also allows for improved analysis with an unstructured correlation matrix. Special focus is given to goodness-of-fit analysis as well as new strategies for selecting the appropriate working correlation structure for QLS and GEE. A chapter on longitudinal binary data tackles recent issues raised in the statistical literature regarding the appropriateness of semi-parametric methods, such as GEE and QLS, for the analysis of binary data; this chapter includes a comparison with the first-order Markov maximum-likelihood (MARK1ML) approach for binary data. Examples throughout the book demonstrate each topic of discussion. In particular, a fully worked out example leads readers from model building and interpretation to the planning stages for a future study (including sample size calculations). The code provided enables readers to replicate many of the examples in Stata, often with corresponding R, SAS, or MATLAB® code offered in the text or on the book’s website.
Book Synopsis Approximative Minimax Estimators in the Linear Regression Model by : Peter Stahlecker
Download or read book Approximative Minimax Estimators in the Linear Regression Model written by Peter Stahlecker and published by . This book was released on 1985 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Minimax Estimation in Linear Regression with Convex Polyhedral Constraints by : P. Stahlecker
Download or read book Minimax Estimation in Linear Regression with Convex Polyhedral Constraints written by P. Stahlecker and published by . This book was released on 1990 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Approximative minimax estimators in the linear regression model by : Jörg Lauterbach
Download or read book Approximative minimax estimators in the linear regression model written by Jörg Lauterbach and published by . This book was released on 1985 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Minimax Estimation of Nonparametric Regression Through White Noise Problem by : Yuhai Wu
Download or read book Minimax Estimation of Nonparametric Regression Through White Noise Problem written by Yuhai Wu and published by . This book was released on 1997 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis An Unexpected Property of Minimax Estimation in the Relative Squared Error Approach to Linear Regression Analysis by : Bernhard F. Arnold
Download or read book An Unexpected Property of Minimax Estimation in the Relative Squared Error Approach to Linear Regression Analysis written by Bernhard F. Arnold and published by . This book was released on 2009 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Approximate minimax estimators in the linear regression model by : Peter Stahlecker
Download or read book Approximate minimax estimators in the linear regression model written by Peter Stahlecker and published by . This book was released on 1986 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Approximative minimax estimators in the linear regression model by : Jörg Lauterbach
Download or read book Approximative minimax estimators in the linear regression model written by Jörg Lauterbach and published by . This book was released on 1985 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt: