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Author : Chris J. Lloyd,M. C. Jones,Australian Graduate School of Management
Publisher : Unknown
Page : 28 pages
File Size : 54,8 Mb
Release : 1999
Category : Distribution (Probability theory)
ISBN : 1862743673
Author : Anonim
Publisher : IMS
Page : 252 pages
File Size : 40,7 Mb
Release : 2006
Category : Nonparametric statistics
ISBN : 0940600668
Author : Eduardo Gil,Eva Gil,Juan Gil,María Ángeles Gil
Publisher : Springer
Page : 917 pages
File Size : 40,9 Mb
Release : 2018-02-28
Category : Technology & Engineering
ISBN : 9783319738482
This book is a tribute to Professor Pedro Gil, who created the Department of Statistics, OR and TM at the University of Oviedo, and a former President of the Spanish Society of Statistics and OR (SEIO). In more than eighty original contributions, it illustrates the extent to which Mathematics can help manage uncertainty, a factor that is inherent to real life. Today it goes without saying that, in order to model experiments and systems and to analyze related outcomes and data, it is necessary to consider formal ideas and develop scientific approaches and techniques for dealing with uncertainty. Mathematics is crucial in this endeavor, as this book demonstrates. As Professor Pedro Gil highlighted twenty years ago, there are several well-known mathematical branches for this purpose, including Mathematics of chance (Probability and Statistics), Mathematics of communication (Information Theory), and Mathematics of imprecision (Fuzzy Sets Theory and others). These branches often intertwine, since different sources of uncertainty can coexist, and they are not exhaustive. While most of the papers presented here address the three aforementioned fields, some hail from other Mathematical disciplines such as Operations Research; others, in turn, put the spotlight on real-world studies and applications. The intended audience of this book is mainly statisticians, mathematicians and computer scientists, but practitioners in these areas will certainly also find the book a very interesting read.
Author : Sam Efromovich
Publisher : CRC Press
Page : 448 pages
File Size : 50,7 Mb
Release : 2018-03-12
Category : Mathematics
ISBN : 9781351679848
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.
Author : Anonim
Publisher : Unknown
Page : 1788 pages
File Size : 45,6 Mb
Release : 2008
Category : Electronic journals
ISBN : UOM:49015003303352
Author : Jiayang Sun
Publisher : Unknown
Page : 248 pages
File Size : 51,8 Mb
Release : 2006
Category : Nonparametric statistics
ISBN : UOM:39015073596531
Author : Anonim
Publisher : Unknown
Page : 802 pages
File Size : 40,5 Mb
Release : 2001
Category : Mathematics
ISBN : UVA:X006089372
Author : Stanford University. Department of Statistics,D. W. Scott,G. R. Terrell
Publisher : Unknown
Page : 48 pages
File Size : 45,6 Mb
Release : 1986
Category : Electronic
ISBN : OCLC:123319753
Nonparametric density estimation requires the specification of smoothing parameters. The demands of statistical objectivity make it highly desirable to base the choice on properties of the data set. This paper introduces some biased cross-validation criteria for selection of smoothing parameters for kernel and histogram density estimators. These criteria are obtained by estimating L sub 2-norms of derivatives of the unknown density and provide slightly biased estimates of the average squared-L sub 2 error or mean integrated squared error. These criteria are roughly the analog of the generalized cross-validation procedure for orthogonal series density estimators. The authors present the relationship of the biased cross-validation procedure to the least squares cross-validation procedure, which provides unbiased estimates of the mean integrated squared error. Both methods are shown to be based on U-statistics. The two methods are compared through theoretical calculation of the noise in the cross-validation functions and corresponding cross validated smoothing parameters, by Monte Carlo simulation, and by example. Surprisingly large gains in asymptotic efficiency are observed between biased and unbiased cross-validation when the underlying density is sufficiently smooth. Reliability of cross-validation for finite samples is discussed. (Author).
Author : Anirban DasGupta
Publisher : Springer Science & Business Media
Page : 796 pages
File Size : 47,7 Mb
Release : 2011-05-17
Category : Mathematics
ISBN : 9781441996343
This book provides a versatile and lucid treatment of classic as well as modern probability theory, while integrating them with core topics in statistical theory and also some key tools in machine learning. It is written in an extremely accessible style, with elaborate motivating discussions and numerous worked out examples and exercises. The book has 20 chapters on a wide range of topics, 423 worked out examples, and 808 exercises. It is unique in its unification of probability and statistics, its coverage and its superb exercise sets, detailed bibliography, and in its substantive treatment of many topics of current importance. This book can be used as a text for a year long graduate course in statistics, computer science, or mathematics, for self-study, and as an invaluable research reference on probabiliity and its applications. Particularly worth mentioning are the treatments of distribution theory, asymptotics, simulation and Markov Chain Monte Carlo, Markov chains and martingales, Gaussian processes, VC theory, probability metrics, large deviations, bootstrap, the EM algorithm, confidence intervals, maximum likelihood and Bayes estimates, exponential families, kernels, and Hilbert spaces, and a self contained complete review of univariate probability.
Author : Lei Sun
Publisher : Unknown
Page : 79 pages
File Size : 48,9 Mb
Release : 2007
Category : Nonparametric statistics
ISBN : 0549087265
New kernel distribution function and kernel density function estimators based on a nonparametric transformation of the data for the purpose of bias reduction are proposed. Asymptotic bias expansions for the new estimators are presented and analyzed. Statistical properties in terms of bias, variance, and mean squared error of the new estimators are investigated with computer simulations.
Author : Rafael Kawka
Publisher : Unknown
Page : 18 pages
File Size : 54,6 Mb
Release : 2014
Category : Electronic
ISBN : OCLC:931817495
Author : Ms.Camelia Minoiu,Sanjay Reddy
Publisher : International Monetary Fund
Page : 36 pages
File Size : 50,6 Mb
Release : 2008-07-01
Category : Social Science
ISBN : 9781451870411
We analyze the performance of kernel density methods applied to grouped data to estimate poverty (as applied in Sala-i-Martin, 2006, QJE). Using Monte Carlo simulations and household surveys, we find that the technique gives rise to biases in poverty estimates, the sign and magnitude of which vary with the bandwidth, the kernel, the number of datapoints, and across poverty lines. Depending on the chosen bandwidth, the $1/day poverty rate in 2000 varies by a factor of 1.8, while the $2/day headcount in 2000 varies by 287 million people. Our findings challenge the validity and robustness of poverty estimates derived through kernel density estimation on grouped data.
Author : Benedikt Funke,Rafael Kawka
Publisher : Unknown
Page : 0 pages
File Size : 40,8 Mb
Release : 2014
Category : Electronic
ISBN : OCLC:931817495
Author : Thomas Blumentritt
Publisher : BoD – Books on Demand
Page : 202 pages
File Size : 55,7 Mb
Release : 2012
Category : Business & Economics
ISBN : 9783844101218
Measuring the degree of association between random variables is a task inherent in many practical applications such as risk management and financial modeling. Well-known measures like Spearman's rho and Kendall's tau can be expressed in terms of the underlying copula only, hence, being independent of the underlying univariate marginal distributions. Opposed to these classical measures of association, mutual information, which is derived from information theory, constitutes a fundamentally different approach of measuring association. Although this measure is likewise independent of the univariate margins, it is not a functional of the copula but of the corresponding copula density. Besides the theoretical properties of mutual information as a measure of multivariate association, possibilities to estimate the copula density based on observations of continuous distributions are investigated. To cope with the effect of boundary bias, new estimators are introduced and existing functionals are generalized to the multivariate case. The performance of these estimators is evaluated in comparison to common kernel density estimation schemes. To facilitate variance estimation by means of resampling methods like bootstrapping, an algorithm is introduced, which significantly reduces computation time in comparison with pre-implemented algorithms. In practical applications, complete continuous data is oftentimes not available to the analyst. Instead, categorial data derived from the underlying continuous distribution may be given. Hence, estimation of the copula and its density based on contingency tables is investigated. The newly developed estimators are employed to derive estimates of Spearman's rho and Kendall's tau and their performance is compared.
Author : Richard A. Tapia,James Robert Thompson
Publisher : Unknown
Page : 196 pages
File Size : 53,9 Mb
Release : 1978
Category : Distribution (Probability theory).
ISBN : UOM:39076006797398