Prediction and Nonparametric Estimation for Time Series with Heavy Tails

Prediction and Nonparametric Estimation for Time Series with Heavy Tails
Author: Peter Hall
Publisher:
Total Pages: 0
Release: 2004
Genre:
ISBN:

Motivated by prediction problems for time series with heavy-tailed marginal distributions, we consider methods based on 'local least absolute deviations' for estimating a regression median from dependent data. Unlike more conventional 'local median' methods, which are in effect based on locally fitting a polynomial of degree 0, techniques founded on local least absolute deviations have quadratic bias right up to the boundary of the design interval. Also in contrast to local least-squares methods based on linear fits, the order of magnitude of variance does not depend on tail-weight of the error distribution. To make these points clear, we develop theory describing local applications to time series of both least-squares and least-absolute-deviations methods, showing for example that, in the case of heavy-tailed data, the conventional local-linear least-squares estimator suffers from an additional bias term as well as increased variance.

Nonparametric Econometrics

Nonparametric Econometrics
Author: Qi Li
Publisher: Princeton University Press
Total Pages: 768
Release: 2023-07-18
Genre: Business & Economics
ISBN: 0691248087

A comprehensive, up-to-date textbook on nonparametric methods for students and researchers Until now, students and researchers in nonparametric and semiparametric statistics and econometrics have had to turn to the latest journal articles to keep pace with these emerging methods of economic analysis. Nonparametric Econometrics fills a major gap by gathering together the most up-to-date theory and techniques and presenting them in a remarkably straightforward and accessible format. The empirical tests, data, and exercises included in this textbook help make it the ideal introduction for graduate students and an indispensable resource for researchers. Nonparametric and semiparametric methods have attracted a great deal of attention from statisticians in recent decades. While the majority of existing books on the subject operate from the presumption that the underlying data is strictly continuous in nature, more often than not social scientists deal with categorical data—nominal and ordinal—in applied settings. The conventional nonparametric approach to dealing with the presence of discrete variables is acknowledged to be unsatisfactory. This book is tailored to the needs of applied econometricians and social scientists. Qi Li and Jeffrey Racine emphasize nonparametric techniques suited to the rich array of data types—continuous, nominal, and ordinal—within one coherent framework. They also emphasize the properties of nonparametric estimators in the presence of potentially irrelevant variables. Nonparametric Econometrics covers all the material necessary to understand and apply nonparametric methods for real-world problems.

Nonparametric Geostatistics

Nonparametric Geostatistics
Author: S. Henley
Publisher: Springer Science & Business Media
Total Pages: 156
Release: 2012-12-06
Genre: Science
ISBN: 9400981171

The ideas in this book have been developed over the past three or four years while I was working at the Institute of Geological Sciences and later for Golder Associates. During that time all of the geological modelling and resource estimation studies I participated in had data that were non-ideal in one respect or another (or just plain 'dirty'): the standard ways of handling the data with kriging or with simpler parametric methods gave reason able results, but always there were nagging doubts and some lack of confidence because of the corners that had to be cut in generat ing a model. The bimodal distribution that was assumed to be 'close enough' to normal; the pattern of rich and poor zones that was not quite a trend yet made the data very non-stationary; and the many plotted variograms that would not fit any standard model variogram: these all contributed to the feeling that there should be something that statistics could say about the cases where hardly any assumptions could be made about the properties ofthe parent population.