Transformations and Bayesian Estimation of Skewed and Heavy-Tailed Densities

Transformations and Bayesian Estimation of Skewed and Heavy-Tailed Densities

Bibliographic Details
Main Author: Bean, Andrew Taylor
Language:English
Published: The Ohio State University / OhioLINK 2017
Subjects:
Statistics
density estimation
transformations
nonparametric statistics
Dirichlet process mixtures
heavy tails
regular variation
Online Access:http://rave.ohiolink.edu/etdc/view?acc_num=osu1503015935192212
id ndltd-OhioLink-oai-etd.ohiolink.edu-osu1503015935192212
record_format oai_dc
spelling ndltd-OhioLink-oai-etd.ohiolink.edu-osu15030159351922122021-08-03T07:03:57Z Transformations and Bayesian Estimation of Skewed and Heavy-Tailed Densities Bean, Andrew Taylor Statistics density estimation transformations nonparametric statistics Dirichlet process mixtures heavy tails regular variation In data analysis applications characterized by large and possibly irregular data sets, nonparametric statistical techniques aim to ensure that, as the sample size grows, all unusual features of the data generating process can be captured. Good large-sample performance can be guaranteed in broad classes of problems. Yet within these broad classes, some problems may be substantially more difficult than others. This fact, long recognized in classical nonparametrics, also holds in the growing field of Bayesian nonparametrics, where flexible prior distributions are developed to allow for an infinite-dimensional set of possible truths.This dissertation studies the Bayesian approach to the classic problem of nonparametric density estimation, in the presence of specific irregularities such as heavy tails and skew. The problem of estimating an unknown probability density is recognized as being harder when the density is skewed or heavy tailed than when it is symmetric and light-tailed. It is more challenging problem for classical kernel density estimators, where the expected squared-error loss is higher for heavier tailed densities. It is also a more challenging problem in Bayesian density estimation, where heavy tails preclude the analytical treatment required to establish a large-sample convergence rate for the popular Dirichlet-Process (DP) mixture model. Our proposed approach addresses these features by incorporating a low-dimensional parametric transformation of the sample, estimated from the data, with the aim of setting up an easier density estimation problem on the transformed scale. This strategy was proposed earlier in combination with kernel density estimators, and we illustrate its usefulness in the Bayesian context. Further, we develop a set of transformations estimated in a way to ensure that the fastest proven convergence rate for the DP mixture is applicable to the transformed problem.The transformation-density estimation technique makes advantageous use of a parametric pre-analysis to address specific irregularities in the data generating process. Since the parametric stage is low-dimensional, and governed by a faster convergence rate, the asymptotic performance of the model is enhanced without slowing down the overall convergence rate. We consider other settings where this recipe for semiparametric analysis --- with parametric sub-analyses designed to address specific irregularities, or to simplify the main nonparametric component of the analysis --- might be beneficial. 2017 English text The Ohio State University / OhioLINK http://rave.ohiolink.edu/etdc/view?acc_num=osu1503015935192212 http://rave.ohiolink.edu/etdc/view?acc_num=osu1503015935192212 unrestricted This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws.
collection NDLTD
language English
sources NDLTD
topic Statistics
density estimation
transformations
nonparametric statistics
Dirichlet process mixtures
heavy tails
regular variation
spellingShingle Statistics
density estimation
transformations
nonparametric statistics
Dirichlet process mixtures
heavy tails
regular variation
Bean, Andrew Taylor
Transformations and Bayesian Estimation of Skewed and Heavy-Tailed Densities
author Bean, Andrew Taylor
author_facet Bean, Andrew Taylor
author_sort Bean, Andrew Taylor
title Transformations and Bayesian Estimation of Skewed and Heavy-Tailed Densities
title_short Transformations and Bayesian Estimation of Skewed and Heavy-Tailed Densities
title_full Transformations and Bayesian Estimation of Skewed and Heavy-Tailed Densities
title_fullStr Transformations and Bayesian Estimation of Skewed and Heavy-Tailed Densities
title_full_unstemmed Transformations and Bayesian Estimation of Skewed and Heavy-Tailed Densities
title_sort transformations and bayesian estimation of skewed and heavy-tailed densities
publisher The Ohio State University / OhioLINK
publishDate 2017
url http://rave.ohiolink.edu/etdc/view?acc_num=osu1503015935192212
work_keys_str_mv AT beanandrewtaylor transformationsandbayesianestimationofskewedandheavytaileddensities
_version_ 1719452847489155072

Similar Items