Quantile Regression in a Varying Coefficient Model

Quantile regression extends the statistical quantities of interest beyond conditional means. The regression has been well developed for linear models but less explored for nonparametric models. In this thesis, we consider the estimation of conditional quantiles in a varying-coefficient model. Quantile functions are estimated by polynomial splines and computed via linear programming. A stepwise model selection algorithm is adopted for knot selection. We show that the spline estimators attain the optimal rate of global convergence under appropriate conditions. We also consider testing the hypothesis of constant coefficients in the varying-coefficient model. The methods can be easily extended to situations where the coefficient functions have to satisfy certain shape constraints such as monotonicity and convexity. The relationships between systolic blood pressure and body mass index and systolic and diastolic blood pressures of UK residents are explored as the examples illustrate the methodology.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Statistics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Kim, Mi-Ok

Contributors dc:contributor

• He, Xuming

• Statistics

Language dc:language

eng

Identifier

(MiAaPQ)AAI3086099

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/87394