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Author | : Clive Loader |
Publisher | : Springer Science & Business Media |
Total Pages | : 290 |
Release | : 2006-05-09 |
Genre | : Mathematics |
ISBN | : 0387227326 |
Download Local Regression and Likelihood Book in PDF, ePub and Kindle
Separation of signal from noise is the most fundamental problem in data analysis, arising in such fields as: signal processing, econometrics, actuarial science, and geostatistics. This book introduces the local regression method in univariate and multivariate settings, with extensions to local likelihood and density estimation. Practical information is also included on how to implement these methods in the programs S-PLUS and LOCFIT.
Author | : Robert Tibshirani |
Publisher | : Ann Arbor, Mich. : University Microfilms International |
Total Pages | : 57 |
Release | : 1984 |
Genre | : Asymptotic efficiencies (Statistics) |
ISBN | : |
Download Local Likelihood Estimation Book in PDF, ePub and Kindle
This paper extends the idea of local averaging to likelihood based models. One such application is to the class of generalized linear models. The author enlarges this class by replacing the covariate from chi beta with an unspecified smooth function. This function is estimated from the data by a technique called Local Likelihood Estimation - a type of local averaging. Multiple covariates are incorporated through a forward stepwise algorithm. The main application discussed however, is to the proportional hazards model of Cox (1972), for censored data, In a number of real data examples, the local likelihood technique proves to be effective in uncovering non-linear dependencies. Finally, the author gives some asymptotic results for local likelihood estimates and provides some methods for inference.
Author | : Francesco Audrino |
Publisher | : |
Total Pages | : 0 |
Release | : 2005 |
Genre | : |
ISBN | : |
Download Local Likelihood for Non-Parametric Arch(1) Models Book in PDF, ePub and Kindle
We propose a local likelihood estimation for the log-transformed ARCH(1) model in the financial field. Our nonparametric estimator is constructed within the likelihood framework for non-Gaussian observations: It is different from standard kernel regression smoothing, where the innovations are assumed to be normally distributed. We derive consistency and asymptotic normality for our estimators and conclude from simulation and real data analysis that the local likelihood estimator has better predictive potential than classical local regression.
Author | : |
Publisher | : |
Total Pages | : |
Release | : 2006 |
Genre | : |
ISBN | : |
Download Spatial Aggregation of Local Likelihood Estimates with Applications to Classification Book in PDF, ePub and Kindle
This paper presents a new method for spatially adaptive local likelihood estimation which applies to a broad class of nonparametric models, including the Gaussian, Poisson and binary response models. The main idea of the method is given a sequence of local likelihood estimates ("weak" estimates), to construct a new aggregated estimate whose pointwise risk is of order of the smallest risk among all "weak" estimates. We also propose a new approach towards selecting the parameters of the procedure by providing the prescribed behavior of the resulting estimate in the simple parametric situation. We establish a number of important theoretical results concerning the optimality of the aggregated estimate. In particular, our "oracle" results claims that its risk is up to some logarithmic multiplier equal to the smallest risk for the given family of estimates. The performance of the procedure is illustrated by application to the classification problem. A numerical study demonstrates its nice performance in simulated and real life examples. -- adaptive weights ; local likelihood ; exponential family ; classification
Author | : Göran Kauermann |
Publisher | : |
Total Pages | : 84 |
Release | : 1995 |
Genre | : Econometrics |
ISBN | : |
Download Local Likelihood Estimation and Bias Reduction in Varying-coefficient Models Book in PDF, ePub and Kindle
Abstract: "Varying coefficient models result from generalized linear models by allowing the parameter of the linear predictor to vary across some additional explanatory quantity called effect modifier. While Hastie & Tibshirani (1993) used spline smoothing techniques in univariate varying-coefficient models here the local likelihood approach is considered within the framework of multivariate generalized models. This approach allows the investigation of asymptotic properties of the estimate. Based on the Taylor expansion of the local likelihood function, consistency and asymptotic normality of the estimates are shown under rather general assuptions. Moreover, a numerically simple additive bias reduction method is proposed. The results are given for discrete as well as for continuous effect modifiers and asymptotically optimal rates of smoothing are derived. In the paper a different normalization of weights used. [sic] Instead of summing up to one the weights are one at the target point and less than one in the neighbourhood. This setting results by theoretical considerations and is supported by simulations showing an improvement of the variance estimation of the estimates for finite sample size. It is easy to see that both normalizations are asymptotically equivalent. An example taken from the German socio-economic panel demonstrates the applicability of the presented results."
Author | : Aaron Kenji Aragaki |
Publisher | : |
Total Pages | : 336 |
Release | : 1995 |
Genre | : |
ISBN | : |
Download A Simple Local Least Squares Approach for Estimating the Regression Function of Binary Response Data and Related Data-driven Bandwidth Selection Procedures Book in PDF, ePub and Kindle
Author | : William Gould |
Publisher | : Stata Press |
Total Pages | : 352 |
Release | : 2010-10-27 |
Genre | : Mathematics |
ISBN | : 9781597180788 |
Download Maximum Likelihood Estimation with Stata, Fourth Edition Book in PDF, ePub and Kindle
Maximum Likelihood Estimation with Stata, Fourth Edition is written for researchers in all disciplines who need to compute maximum likelihood estimators that are not available as prepackaged routines. Readers are presumed to be familiar with Stata, but no special programming skills are assumed except in the last few chapters, which detail how to add a new estimation command to Stata. The book begins with an introduction to the theory of maximum likelihood estimation with particular attention on the practical implications for applied work. Individual chapters then describe in detail each of the four types of likelihood evaluator programs and provide numerous examples, such as logit and probit regression, Weibull regression, random-effects linear regression, and the Cox proportional hazards model. Later chapters and appendixes provide additional details about the ml command, provide checklists to follow when writing evaluators, and show how to write your own estimation commands.
Author | : Paul P. Eggermont |
Publisher | : Springer Science & Business Media |
Total Pages | : 580 |
Release | : 2009-06-02 |
Genre | : Mathematics |
ISBN | : 0387689028 |
Download Maximum Penalized Likelihood Estimation Book in PDF, ePub and Kindle
Unique blend of asymptotic theory and small sample practice through simulation experiments and data analysis. Novel reproducing kernel Hilbert space methods for the analysis of smoothing splines and local polynomials. Leading to uniform error bounds and honest confidence bands for the mean function using smoothing splines Exhaustive exposition of algorithms, including the Kalman filter, for the computation of smoothing splines of arbitrary order.
Author | : P. Groeneboom |
Publisher | : Birkhäuser |
Total Pages | : 129 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3034886217 |
Download Information Bounds and Nonparametric Maximum Likelihood Estimation Book in PDF, ePub and Kindle
This book contains the lecture notes for a DMV course presented by the authors at Gunzburg, Germany, in September, 1990. In the course we sketched the theory of information bounds for non parametric and semiparametric models, and developed the theory of non parametric maximum likelihood estimation in several particular inverse problems: interval censoring and deconvolution models. Part I, based on Jon Wellner's lectures, gives a brief sketch of information lower bound theory: Hajek's convolution theorem and extensions, useful minimax bounds for parametric problems due to Ibragimov and Has'minskii, and a recent result characterizing differentiable functionals due to van der Vaart (1991). The differentiability theorem is illustrated with the examples of interval censoring and deconvolution (which are pursued from the estimation perspective in part II). The differentiability theorem gives a way of clearly distinguishing situations in which 1 2 the parameter of interest can be estimated at rate n / and situations in which this is not the case. However it says nothing about which rates to expect when the functional is not differentiable. Even the casual reader will notice that several models are introduced, but not pursued in any detail; many problems remain. Part II, based on Piet Groeneboom's lectures, focuses on non parametric maximum likelihood estimates (NPMLE's) for certain inverse problems. The first chapter deals with the interval censoring problem.
Author | : Jeffrey S. Simonoff |
Publisher | : Springer Science & Business Media |
Total Pages | : 349 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461240263 |
Download Smoothing Methods in Statistics Book in PDF, ePub and Kindle
Focussing on applications, this book covers a very broad range, including simple and complex univariate and multivariate density estimation, nonparametric regression estimation, categorical data smoothing, and applications of smoothing to other areas of statistics. It will thus be of particular interest to data analysts, as arguments generally proceed from actual data rather than statistical theory, while the "Background Material" sections will interest statisticians studying the field. Over 750 references allow researchers to find the original sources for more details, and the "Computational Issues" sections provide sources for statistical software that use the methods discussed. Each chapter includes exercises with a heavily computational focus based upon the data sets used in the book, making it equally suitable as a textbook for a course in smoothing.