Efficient Estimation of an Additive Quantile Regression Model

In this paper, two non-parametric estimators are proposed for estimating the components of an additive quantile regression model. The first estimator is a computationally convenient approach which can be viewed as a more viable alternative to existing kernel-based approaches. The second estimator in...

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Bibliographic Details
Published in:Scandinavian journal of statistics 2011-03, Vol.38 (1), p.46-62
Main Authors: CHENG, YEBIN, DE GOOIJER, JAN G., ZEROM, DAWIT
Format: Article
Language:English
Subjects:
additive models
Asymptotic methods
Asymptotic properties
Data smoothing
dependent data
Estimating techniques
Estimators
Exact sciences and technology
General topics
internalized kernel smoother
Linear inference, regression
local polynomial
Mathematics
oracle efficiency
Oracles
Polynomials
Probability and statistics
Probability theory and stochastic processes
Quantile regression
Quantum efficiency
Regression analysis
Sciences and techniques of general use
Statistical variance
Statistics
Stochastic processes
Studies
Travel time
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Summary:In this paper, two non-parametric estimators are proposed for estimating the components of an additive quantile regression model. The first estimator is a computationally convenient approach which can be viewed as a more viable alternative to existing kernel-based approaches. The second estimator involves sequential fitting by univariate local polynomial quantile regressions for each additive component with the other additive components replaced by the corresponding estimates from the first estimator. The purpose of the extra local averaging is to reduce the variance of the first estimator. We show that the second estimator achieves oracle efficiency in the sense that each estimated additive component has the same variance as in the case when all other additive components were known. Asymptotic properties are derived for both estimators under dependent processes that are strictly stationary and absolutely regular. We also provide a demonstrative empirical application of additive quantile models to ambulance travel times.
ISSN:0303-6898
1467-9469
DOI:10.1111/j.1467-9469.2010.00706.x