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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 : 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 : Gwennaelle Mabon
Publisher :
ISBN 13 :
Total Pages : 23 pages
Book Rating : 4.:/5 (931 download)
Download or read book Adaptive Density Estimation in Deconvolution Problems with Unknown Error Distribution written by Gwennaelle Mabon and published by . This book was released on 2013 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 : Julie P. McIntyre
Publisher :
ISBN 13 :
Total Pages : 118 pages
Book Rating : 4.:/5 (528 download)
Download or read book Density Deconvolution with Replicate Measurements and Auxiliary Data written by Julie P. McIntyre and published by . This book was released on 2003 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: Keywords: deconvolution, measurement error, density estimation.
Author : Yue Chang
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (18 download)
Download or read book Variational Approximations for Density Deconvolution written by Yue Chang and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis considers the problem of density estimation when the variables of interest are subject to measurement error. The measurement error is assumed to be additive and homoscedastic. We specify the density of interest by a Dirichlet Process Mixture Model and establish variational approximation approaches to the density deconvolution problem. Gaussian and Laplacian error distributions are considered, which are representatives of supersmooth and ordinary smooth distributions, respectively. We develop two variational approximation algorithms for Gaussian error deconvolution and one variational approximation algorithm for Laplacian error deconvolution. Their performances are compared to deconvoluting kernels and Monte Carlo Markov Chain method by simulation experiments. A conjecture based on hidden variables categorization is proposed to explain why two variational approximation algorithms for Gaussian error deconvolution perform differently. We establish a stochastic variational approximation algorithm for Gaussian error deconvolution, which improves the performance of variational approximation algorithm and performs as well as MCMC method at faster speed. The stochastic variational approximation algorithm is applied to simulation experiments and an example of physical activity measurements.
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 : 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 : A. J. van Es
Publisher :
ISBN 13 :
Total Pages : 158 pages
Book Rating : 4.3/5 (91 download)
Download or read book Aspects of Nonparametric Density Estimation written by A. J. van Es and published by . This book was released on 1991 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Raymond J. Carroll
Publisher :
ISBN 13 :
Total Pages : 8 pages
Book Rating : 4.:/5 (227 download)
Download or read book Optimal Rates of Convergence for Deconvolving a Density written by Raymond J. Carroll and published by . This book was released on 1988 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: Suppose we observe the sum of two independent random variables X and Z, where Z denotes measurement error and has a known distribution, and where the unknown density f of X is to be estimated. It is shown that if Z is normally distributed and if f has k bounded derivatives, then the fastest attainable convergence rate of any nonparametric estimator of f is only (log n)-k/1. Therefore deconvolution with normal errors may not be a practical proposition. Other error distributions are also treated. Stefanski-Carroll (1978b) estimators achieve the optimal rates. Our results have versions for multiplicative errors, where they imply that even optimal rates are exceptionally slow. Keywords: Deconvolution, Density estimation, Errors variables, Measurement error, Rates Convergence. (MJM).
Author : Nicolai Bissantz
Publisher :
ISBN 13 :
Total Pages : 37 pages
Book Rating : 4.:/5 (254 download)
Download or read book Nonparametric Confidence Bands in Deconvolution Density Estimation written by Nicolai Bissantz and published by . This book was released on 2007 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 : Ramchandra Rimal
Publisher :
ISBN 13 :
Total Pages : 132 pages
Book Rating : 4.:/5 (122 download)
Download or read book Estimation and Clustering for Network and Indirect Data written by Ramchandra Rimal and published by . This book was released on 2020 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first part of the dissertation studies a density deconvolution problem with small Berkson errors. In this setting, the data is not available directly but rather in the form of convolution and one needs to estimate the convolution of the unknown density with Berkson errors. While it is known that the Berkson errors improve the precision of the reconstruction, it does not necessarily happen when Berkson errors are small. Furthermore, the choice of bandwidth in density estimation has been an open problem so far. In this dissertation, we provide an in-depth study of the choice of the bandwidth which leads to the optimal error rates.
Author : Michael H. Neumann
Publisher :
ISBN 13 :
Total Pages : 26 pages
Book Rating : 4.:/5 (632 download)
Download or read book On the Effect of Estimating the Error Density in Nonparametric Deconvolution written by Michael H. Neumann and published by . This book was released on 1995 with total page 26 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 : Raymond J. Carroll
Publisher : CRC Press
ISBN 13 : 1420010131
Total Pages : 484 pages
Book Rating : 4.4/5 (2 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 2006-06-21 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: It's been over a decade since the first edition of Measurement Error in Nonlinear Models splashed onto the scene, and research in the field has certainly not cooled in the interim. In fact, quite the opposite has occurred. As a result, Measurement Error in Nonlinear Models: A Modern Perspective, Second Edition has been revamped and ex
Author : Sam Efromovich
Publisher : CRC Press
ISBN 13 : 1351679848
Total Pages : 448 pages
Book Rating : 4.3/5 (516 download)
Download or read book Missing and Modified Data in Nonparametric Estimation written by Sam Efromovich and published by CRC Press. This book was released on 2018-03-12 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a systematic and unified approach for modern nonparametric treatment of missing and modified data via examples of density and hazard rate estimation, nonparametric regression, filtering signals, and time series analysis. All basic types of missing at random and not at random, biasing, truncation, censoring, and measurement errors are discussed, and their treatment is explained. Ten chapters of the book cover basic cases of direct data, biased data, nondestructive and destructive missing, survival data modified by truncation and censoring, missing survival data, stationary and nonstationary time series and processes, and ill-posed modifications. The coverage is suitable for self-study or a one-semester course for graduate students with a prerequisite of a standard course in introductory probability. Exercises of various levels of difficulty will be helpful for the instructor and self-study. The book is primarily about practically important small samples. It explains when consistent estimation is possible, and why in some cases missing data should be ignored and why others must be considered. If missing or data modification makes consistent estimation impossible, then the author explains what type of action is needed to restore the lost information. The book contains more than a hundred figures with simulated data that explain virtually every setting, claim, and development. The companion R software package allows the reader to verify, reproduce and modify every simulation and used estimators. This makes the material fully transparent and allows one to study it interactively. Sam Efromovich is the Endowed Professor of Mathematical Sciences and the Head of the Actuarial Program at the University of Texas at Dallas. He is well known for his work on the theory and application of nonparametric curve estimation and is the author of Nonparametric Curve Estimation: Methods, Theory, and Applications. Professor Sam Efromovich is a Fellow of the Institute of Mathematical Statistics and the American Statistical Association.
