Quantile Regression in a Varying Coefficient Model
Kim, Mi-Ok
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https://hdl.handle.net/2142/87394
Description
Title
Quantile Regression in a Varying Coefficient Model
Author(s)
Kim, Mi-Ok
Issue Date
2003
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
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.
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