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Author :
Publisher :
ISBN 13 :
Total Pages : 290 pages
Book Rating : 4.:/5 (931 download)
Download or read book Deconvolution Kernel Density and Regression Estimation written by and published by . This book was released on 2011 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Alexander Meister
Publisher : Springer Science & Business Media
ISBN 13 : 3540875573
Total Pages : 211 pages
Book Rating : 4.5/5 (48 download)
Download or read book Deconvolution Problems in Nonparametric Statistics written by Alexander Meister and published by Springer Science & Business Media. This book was released on 2009-12-24 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: Deconvolution problems occur in many ?elds of nonparametric statistics, for example, density estimation based on contaminated data, nonparametric - gression with errors-in-variables, image and signal deblurring. During the last two decades, those topics have received more and more attention. As appli- tions of deconvolution procedures concern many real-life problems in eco- metrics, biometrics, medical statistics, image reconstruction, one can realize an increasing number of applied statisticians who are interested in nonpa- metric deconvolution methods; on the other hand, some deep results from Fourier analysis, functional analysis, and probability theory are required to understand the construction of deconvolution techniques and their properties so that deconvolution is also particularly challenging for mathematicians. Thegeneraldeconvolutionprobleminstatisticscanbedescribedasfollows: Our goal is estimating a function f while any empirical access is restricted to some quantity h = f?G = f(x?y)dG(y), (1. 1) that is, the convolution of f and some probability distribution G. Therefore, f can be estimated from some observations only indirectly. The strategy is ˆ estimating h ?rst; this means producing an empirical version h of h and, then, ˆ applying a deconvolution procedure to h to estimate f. In the mathematical context, we have to invert the convolution operator with G where some reg- ˆ ularization is required to guarantee that h is contained in the invertibility ˆ domain of the convolution operator. The estimator h has to be chosen with respect to the speci?c statistical experiment.
Author : Achilleas Achilleos
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (784 download)
Download or read book Deconvolution Kernal Density and Regression Estimation written by Achilleas Achilleos and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : B. van Es
Publisher :
ISBN 13 :
Total Pages : 18 pages
Book Rating : 4.:/5 (192 download)
Download or read book Some Thoughts Ion the Asymptotics of the Deconvolution Kernel Density Estimator written by B. van Es and published by . This book was released on 2008 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Artur Gramacki
Publisher : Springer
ISBN 13 : 3319716883
Total Pages : 197 pages
Book Rating : 4.3/5 (197 download)
Download or read book Nonparametric Kernel Density Estimation and Its Computational Aspects written by Artur Gramacki and published by Springer. This book was released on 2017-12-21 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes computational problems related to kernel density estimation (KDE) – one of the most important and widely used data smoothing techniques. A very detailed description of novel FFT-based algorithms for both KDE computations and bandwidth selection are presented. The theory of KDE appears to have matured and is now well developed and understood. However, there is not much progress observed in terms of performance improvements. This book is an attempt to remedy this. The book primarily addresses researchers and advanced graduate or postgraduate students who are interested in KDE and its computational aspects. The book contains both some background and much more sophisticated material, hence also more experienced researchers in the KDE area may find it interesting. The presented material is richly illustrated with many numerical examples using both artificial and real datasets. Also, a number of practical applications related to KDE are presented.
Author : Albertus Jacob Es
Publisher :
ISBN 13 :
Total Pages : 22 pages
Book Rating : 4.:/5 (778 download)
Download or read book Asymptotic Normality of the Deconvolution Kernel Density Estimator Under the Vanishing Error Variance written by Albertus Jacob Es and published by . This book was released on 2009 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Marie Davidian
Publisher : Springer
ISBN 13 : 3319058010
Total Pages : 599 pages
Book Rating : 4.3/5 (19 download)
Download or read book The Work of Raymond J. Carroll written by Marie Davidian and published by Springer. This book was released on 2014-06-06 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains Raymond J. Carroll's research and commentary on its impact by leading statisticians. Each of the seven main parts focuses on a key research area: Measurement Error, Transformation and Weighting, Epidemiology, Nonparametric and Semiparametric Regression for Independent Data, Nonparametric and Semiparametric Regression for Dependent Data, Robustness, and other work. The seven subject areas reviewed in this book were chosen by Ray himself, as were the articles representing each area. The commentaries not only review Ray’s work, but are also filled with history and anecdotes. Raymond J. Carroll’s impact on statistics and numerous other fields of science is far-reaching. His vast catalog of work spans from fundamental contributions to statistical theory to innovative methodological development and new insights in disciplinary science. From the outset of his career, rather than taking the “safe” route of pursuing incremental advances, Ray has focused on tackling the most important challenges. In doing so, it is fair to say that he has defined a host of statistics areas, including weighting and transformation in regression, measurement error modeling, quantitative methods for nutritional epidemiology and non- and semiparametric regression.
Author : Chi-Yang Chu
Publisher :
ISBN 13 :
Total Pages : 65 pages
Book Rating : 4.:/5 (999 download)
Download or read book Applied Nonparametric Density and Regression Estimation with Discrete Data written by Chi-Yang Chu and published by . This book was released on 2017 with total page 65 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bandwidth selection plays an important role in kernel density estimation. Least-squares cross-validation and plug-in methods are commonly used as bandwidth selectors for the continuous data setting. The former is a data-driven approach and the latter requires a priori assumptions about the unknown distribution of the data. A benefit from the plug-in method is its relatively quick computation and hence it is often used for preliminary analysis. However, we find that much less is known about the plug-in method in the discrete data setting and this motivates us to propose a plug-in bandwidth selector. A related issue is undersmoothing in kernel density estimation. Least-squares cross-validation is a popular bandwidth selector, but in many applied situations, it tends to select a relatively small bandwidth, or undersmooths. The literature suggests several methods to solve this problem, but most of them are the modifications of extant error criterions for continuous variables. Here we discuss this problem in the discrete data setting and propose non-geometric discrete kernel functions as a possible solution. This issue also occurs in kernel regression estimation. Our proposed bandwidth selector and kernel functions perform well in simulated and real data.
Author : Janet Nakarmi
Publisher :
ISBN 13 :
Total Pages : 86 pages
Book Rating : 4.:/5 (982 download)
Download or read book On Variable Bandwidth Kernel Density and Regression Estimation Dissertation written by Janet Nakarmi and published by . This book was released on 2016 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study the ideal variable bandwidth kernel density estimator introduced by McKay (1993) and the plug-in practical version of the variable bandwidth kernel density estimator with two sequences of bandwidths as in Ginè and Sang (2013).We estimate the variance of the variable bandwidth kernel density estimator. Based on the exact formula of the bias and the variance of the variable bandwidth kernel density estimator, we develop the optimal bandwidth selection of the true variable bandwidth kernel density estimator. Furthermore, we present the central limit theorem of the true variable bandwidth kernel density estimator. We also propose a new variable bandwidth kernel regression estimator and estimate the bias and propose the central limit theorems for its ideal and true versions. For the one dimensional case, the order of the bias and variance is same for the variable bandwidth kernel density estimator and for the proposed variable bandwidth kernel regression estimator. Since we use the order of the bias and variance to find the optimal bandwidth, the optimal bandwidth for these estimators are also the same. Comparing the integrated mean square error of the variable bandwidth kernel density estimator (the variable bandwidth kernel regression estimator) with the classical kernel density estimator (the Nadaraya-Watson estimator), we find that the variable bandwidth kernel estimators have a faster rate of convergence. Furthermore, we prove that these variable bandwidth kernel estimators converge to normal distribution.
Author : Nathaniel A. Litton
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (688 download)
Download or read book Deconvolution in Random Effects Models Via Normal Mixtures written by Nathaniel A. Litton and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation describes a minimum distance method for density estimation when the variable of interest is not directly observed. It is assumed that the underlying target density can be well approximated by a mixture of normals. The method compares a density estimate of observable data with a density of the observable data induced from assuming the target density can be written as a mixture of normals. The goal is to choose the parameters in the normal mixture that minimize the distance between the density estimate of the observable data and the induced density from the model. The method is applied to the deconvolution problem to estimate the density of Xi when the variable Yi=Xi+Zi, i=1 ..., n, is observed, and the density of Zi is known. Additionally, it is applied to a location random effects model to estimate the density of Zij when the observable quantities are p data sets of size n given by Zij=[alpha]i+[gamma]Zij, i=1 ..., p, j=1 ..., n, where the densities of [alpha]i and Zij are both unknown. The performance of the minimum distance approach in the measurement error model is compared with the deconvoluting kernel density estimator of Stefanski and Carroll (1990). In the location random effects model, the minimum distance estimator is compared with the explicit characteristic function inversion method from Hall and Yao (2003). In both models, the methods are compared using simulated and real data sets. In the simulations, performance is evaluated using an integrated squared error criterion. Results indicate that the minimum distance methodology is comparable to the deconvoluting kernel density estimator and outperforms the explicit characteristic function inversion method.
Author : G.G Roussas
Publisher : Springer Science & Business Media
ISBN 13 : 9401132224
Total Pages : 691 pages
Book Rating : 4.4/5 (11 download)
Download or read book Nonparametric Functional Estimation and Related Topics written by G.G Roussas and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 691 pages. Available in PDF, EPUB and Kindle. Book excerpt: About three years ago, an idea was discussed among some colleagues in the Division of Statistics at the University of California, Davis, as to the possibility of holding an international conference, focusing exclusively on nonparametric curve estimation. The fruition of this idea came about with the enthusiastic support of this project by Luc Devroye of McGill University, Canada, and Peter Robinson of the London School of Economics, UK. The response of colleagues, contacted to ascertain interest in participation in such a conference, was gratifying and made the effort involved worthwhile. Devroye and Robinson, together with this editor and George Metakides of the University of Patras, Greece and of the European Economic Communities, Brussels, formed the International Organizing Committee for a two week long Advanced Study Institute (ASI) sponsored by the Scientific Affairs Division of the North Atlantic Treaty Organization (NATO). The ASI was held on the Greek Island of Spetses between July 29 and August 10, 1990. Nonparametric functional estimation is a central topic in statistics, with applications in numerous substantive fields in mathematics, natural and social sciences, engineering and medicine. While there has been interest in nonparametric functional estimation for many years, this has grown of late, owing to increasing availability of large data sets and the ability to process them by means of improved computing facilities, along with the ability to display the results by means of sophisticated graphical procedures.
Author : Ming-Chung Liu
Publisher :
ISBN 13 :
Total Pages : 222 pages
Book Rating : 4.:/5 (174 download)
Download or read book Nonparametric Density Function Estimation and the Deconvolution Problem written by Ming-Chung Liu and published by . This book was released on 1987 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Christian Wagner
Publisher :
ISBN 13 :
Total Pages : 170 pages
Book Rating : 4.:/5 (436 download)
Download or read book Deconvolution Problems in Density Estimation written by Christian Wagner and published by . This book was released on 2009 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : W. Härdle
Publisher : Springer Science & Business Media
ISBN 13 : 3662050218
Total Pages : 413 pages
Book Rating : 4.6/5 (62 download)
Download or read book Applied Quantitative Finance written by W. Härdle and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents solutions for many practical problems in quantitative finance. The e-book design of the text connects theory and computational tools in an innovative way. All "quantlets" for calculation of examples in the text are executable on an XploRe Quantlet Server (XQS) and can be modified by the reader via the internet. The electronic edition can be downloaded from the web.
Author : José E. Chacón
Publisher : CRC Press
ISBN 13 : 0429939140
Total Pages : 226 pages
Book Rating : 4.4/5 (299 download)
Download or read book Multivariate Kernel Smoothing and Its Applications written by José E. Chacón and published by CRC Press. This book was released on 2018-05-08 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kernel smoothing has greatly evolved since its inception to become an essential methodology in the data science tool kit for the 21st century. Its widespread adoption is due to its fundamental role for multivariate exploratory data analysis, as well as the crucial role it plays in composite solutions to complex data challenges. Multivariate Kernel Smoothing and Its Applications offers a comprehensive overview of both aspects. It begins with a thorough exposition of the approaches to achieve the two basic goals of estimating probability density functions and their derivatives. The focus then turns to the applications of these approaches to more complex data analysis goals, many with a geometric/topological flavour, such as level set estimation, clustering (unsupervised learning), principal curves, and feature significance. Other topics, while not direct applications of density (derivative) estimation but sharing many commonalities with the previous settings, include classification (supervised learning), nearest neighbour estimation, and deconvolution for data observed with error. For a data scientist, each chapter contains illustrative Open data examples that are analysed by the most appropriate kernel smoothing method. The emphasis is always placed on an intuitive understanding of the data provided by the accompanying statistical visualisations. For a reader wishing to investigate further the details of their underlying statistical reasoning, a graduated exposition to a unified theoretical framework is provided. The algorithms for efficient software implementation are also discussed. José E. Chacón is an associate professor at the Department of Mathematics of the Universidad de Extremadura in Spain. Tarn Duong is a Senior Data Scientist for a start-up which provides short distance carpooling services in France. Both authors have made important contributions to kernel smoothing research over the last couple of decades.
Author : Grace Y. Yi
Publisher : CRC Press
ISBN 13 : 1351588591
Total Pages : 648 pages
Book Rating : 4.3/5 (515 download)
Download or read book Handbook of Measurement Error Models written by Grace Y. Yi and published by CRC Press. This book was released on 2021-09-28 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt: Measurement error arises ubiquitously in applications and has been of long-standing concern in a variety of fields, including medical research, epidemiological studies, economics, environmental studies, and survey research. While several research monographs are available to summarize methods and strategies of handling different measurement error problems, research in this area continues to attract extensive attention. The Handbook of Measurement Error Models provides overviews of various topics on measurement error problems. It collects carefully edited chapters concerning issues of measurement error and evolving statistical methods, with a good balance of methodology and applications. It is prepared for readers who wish to start research and gain insights into challenges, methods, and applications related to error-prone data. It also serves as a reference text on statistical methods and applications pertinent to measurement error models, for researchers and data analysts alike. Features: Provides an account of past development and modern advancement concerning measurement error problems Highlights the challenges induced by error-contaminated data Introduces off-the-shelf methods for mitigating deleterious impacts of measurement error Describes state-of-the-art strategies for conducting in-depth research
Author : Raymond J. Carroll
Publisher : CRC Press
ISBN 13 : 9780412047213
Total Pages : 334 pages
Book Rating : 4.0/5 (472 download)
Download or read book Measurement Error in Nonlinear Models written by Raymond J. Carroll and published by CRC Press. This book was released on 1995-07-06 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides an up-to-date discussion of analysis strategies for regression problems in which predictor variables are measured with errors. The analysis of nonlinear regression models includes generalized linear models, transform-both-sides models and quasilikelihood and variance function problems. The text concentrates on the general ideas and strategies of estimation and inference rather than being concerned with a specific problem. Measurement error occurs in many fields, such as biometry, epidemiology and economics. In particular, the book contains a large number of epidemiological examples. An outline of strategies for handling progressively more difficult problems is also provided.
