Power Transformation Towards Linear or Partially Linear Quantile Regression Models

Mu, Yunming

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https://hdl.handle.net/2142/87401 Copy

Description

Title

Power Transformation Towards Linear or Partially Linear Quantile Regression Models

Author(s)

Mu, Yunming

Issue Date

2005

Doctoral Committee Chair(s)

He, Xuming

Department of Study

Statistics

Discipline

Statistics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

Statistics

Language

eng

Abstract

In this thesis, we consider a family of parametric power transformations for the dependent variable such that a linear or partially linear quantile regression model holds after transformation. The two models being considered are the power-transformed linear quantile regression model and power-transformed partially linear quantile regression model, respectively. We use a cusum process of residuals to measure lack of fit for a given quantile function. A power transformation is chosen to minimize the lack of fit. For the power-transformed linear quantile regression model, we show that the proposed estimator is consistent and asymptotically normal under some mild conditions. We demonstrate that the proposed approach works better than competing methods in the presence of heteroscedasticity and heavy-tails. Inferences about the transformation parameter and about the covariate effects are considered mathematically as well as empirically. A test for the adequacy of the power-transformation models is also proposed. For the power-transformed partially linear quantile regression model, we establish the consistency property for the proposed estimator.

Graduation Semester

2005

Type of Resource

text

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http://hdl.handle.net/2142/87401

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