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Author: David X. Chan Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
This article considers the estimation of a regression model with Gaussian errors, where the mean and the log variance are modeled as a linear combination of explanatory variables. We consider Bayesian variable selection priors and model averaging to obtain efficient estimators when the number of explanatory variables is large. To make the model semiparametric using this framework we allow explanatory variables to enter the mean and log variance models flexibly by representing a covariate effect as a linear combination of basis functions. Our methodology for estimating flexible effects is locally adaptive in the sense that it works well when the flexible effects vary rapidly in some parts of the predictor space but only slowly in other parts. The whole model is estimated using a Markov chain simulation method that samples the posterior distribution with coefficients in the mean model integrated out analytically and highly dependent parameters generated in blocks. The methodology in the paper is applied to a number of simulated and real examples and is shown to work well.
Author: David X. Chan Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
This article considers the estimation of a regression model with Gaussian errors, where the mean and the log variance are modeled as a linear combination of explanatory variables. We consider Bayesian variable selection priors and model averaging to obtain efficient estimators when the number of explanatory variables is large. To make the model semiparametric using this framework we allow explanatory variables to enter the mean and log variance models flexibly by representing a covariate effect as a linear combination of basis functions. Our methodology for estimating flexible effects is locally adaptive in the sense that it works well when the flexible effects vary rapidly in some parts of the predictor space but only slowly in other parts. The whole model is estimated using a Markov chain simulation method that samples the posterior distribution with coefficients in the mean model integrated out analytically and highly dependent parameters generated in blocks. The methodology in the paper is applied to a number of simulated and real examples and is shown to work well.
Author: Edward Greenberg Publisher: Cambridge University Press ISBN: 1139789333 Category : Business & Economics Languages : en Pages : 271
Book Description
This textbook explains the basic ideas of subjective probability and shows how subjective probabilities must obey the usual rules of probability to ensure coherency. It defines the likelihood function, prior distributions and posterior distributions. It explains how posterior distributions are the basis for inference and explores their basic properties. Various methods of specifying prior distributions are considered, with special emphasis on subject-matter considerations and exchange ability. The regression model is examined to show how analytical methods may fail in the derivation of marginal posterior distributions. The remainder of the book is concerned with applications of the theory to important models that are used in economics, political science, biostatistics and other applied fields. New to the second edition is a chapter on semiparametric regression and new sections on the ordinal probit, item response, factor analysis, ARCH-GARCH and stochastic volatility models. The new edition also emphasizes the R programming language.
Author: D. Ruppert Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
The conditional variance function in a heteroscedastic, nonparametric regression model is estimated by linear smoothing of squared residuals. Attention is focussed on local polynomial smoothers. Both the mean and variance functions are assumed to be smooth, but neither is assumed to be in a parametric family. The effect of preliminary estimation of the mean is studied, and a "degrees of freedom" is proposed. The corrected method is shown to be adaptive in the sense that the variance function can be estimated with the same asymptotic mean and variance as if the mean function were known. A proposal is made for using standard bandwidth selectors for estimating both the mean and variance functions. The proposal is illustrated with data from the LIDAR method of measuring atmospheric pollutants and from turbulence model computations.
Author: Raymond J. Carroll Publisher: ISBN: Category : Estimation theory Languages : en Pages : 29
Book Description
This document investigates the limiting behavior of a class of one-step M-estimators in heteroscedastic regression models. The mean function is assumed to be known up to parameters, but the variance function is considered an unknown function of a dimensional vector. The variance function is to be estimated nonparametrically by a function of the absolute residuals from the current fit to the mean. Under a variety of conditions when the estimates adapt for scale, i.e., the regression parameter is estimated just as well as if the scale function was known. Connections with the theory of optimal semiparametric estimation are made. (Author).
Author: Odile Pons Publisher: World Scientific ISBN: 9811272859 Category : Mathematics Languages : en Pages : 259
Book Description
Nonparametric kernel estimators apply to the statistical analysis of independent or dependent sequences of random variables and for samples of continuous or discrete processes. The optimization of these procedures is based on the choice of a bandwidth that minimizes an estimation error and the weak convergence of the estimators is proved. This book introduces new mathematical results on statistical methods for the density and regression functions presented in the mathematical literature and for functions defining more complex models such as the models for the intensity of point processes, for the drift and variance of auto-regressive diffusions and the single-index regression models.This second edition presents minimax properties with Lp risks, for a real p larger than one, and optimal convergence results for new kernel estimators of function defining processes: models for multidimensional variables, periodic intensities, estimators of the distribution functions of censored and truncated variables, estimation in frailty models, estimators for time dependent diffusions, for spatial diffusions and for diffusions with stochastic volatility.
Author: Lukasz Delong Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
Regression modeling for insurance pricing mostly focuses on mean estimation. Using a strictly consistent loss function implies that the mean estimates are asymptotically correct. However, this is a limiting statement and insurance prices are calculated on finite samples. It is known that under heteroskedasticity suitable variance estimates can significantly improve the regression model estimation. In this paper we investigate isotonic regression which is a non-parametric rank-preserving regression approach.This isotonic regression is used to (1) explore the power variance parameter of the variance function within Tweedie's family of distributions, (2) derive a semi-parametric bootstrap under heteroskedasticity, (3) provide a test for auto-calibration, (4) explore a quasi-likelihood approach to benefit from best-asymptotic estimation, (5) deal with several difficulties under lognormal assumptions. In all these problems we verify that variance estimation using an isotonic regression is very beneficial.
Author: Wolfgang Karl Härdle Publisher: Springer Science & Business Media ISBN: 364217146X Category : Mathematics Languages : en Pages : 317
Book Description
The statistical and mathematical principles of smoothing with a focus on applicable techniques are presented in this book. It naturally splits into two parts: The first part is intended for undergraduate students majoring in mathematics, statistics, econometrics or biometrics whereas the second part is intended to be used by master and PhD students or researchers. The material is easy to accomplish since the e-book character of the text gives a maximum of flexibility in learning (and teaching) intensity.
Author: David X. Chan
Author: David X. Chan
Author: Douglas Gardiner Steigerwald
Author: Edward Greenberg
Author: D. Ruppert
Author: David Ruppert
Author: Raymond J. Carroll
Author: Odile Pons
Author: 
Author: Lukasz Delong
Author: Wolfgang Karl Härdle