|
Activity Number:
|
207
|
|
Type:
|
Topic Contributed
|
|
Date/Time:
|
Tuesday, August 13, 2002 : 10:30 AM to 12:20 PM
|
|
Sponsor:
|
IMS
|
| Abstract - #300605 |
|
Title:
|
Estimation of Conditional Quantile Functions in a Varying Coefficient Model
|
|
Author(s):
|
Mi-Ok Kim*+ and Xuming He
|
|
Affiliation(s):
|
University of Illinois, Urbana-Champaign and University of Illinois, Urbana-Champaign
|
|
Address:
|
725 South Wright St. Room101, Champaign, Illinois, 61820, USA
|
|
Keywords:
|
Quantile regression; ; Varying-coefficient model; ; Constrained regression; ; Convergence rate
|
|
Abstract:
|
Quantile regression extends the statistical quantities of interest beyond the conditional means. While it has been well-developed for linear models, the regression has been less explored for nonparametric models. This paper expands the previous work by adopting a varying-coefficient model, which has succeeded as a powerful nonparametric data analytic tool in the least-squares regression. Quantile functions are estimated by splines and computed via linear programming. A stepwise model selection algorithm is adopted for knot selection of the splines. We show that the spline estimators attain the optimal rate of global convergence under appropriate conditions. The methods can be easily extended to situations where the coefficient functions have to satisfy certain shape constraints such as monotonicity and convexity. An example is provided to illustrate the methodology where the relationship between systolic and diastolic blood pressures of UK residents is explored.
|
