Journal article
Estimation of conditional quantiles by a new smoothing approximation of asymmetric loss functions
Statistics and computing, Vol.15(1), pp.5-11
01/01/2005
DOI: 10.1007/s11222-005-4785-9
Abstract
In this paper, nonparametric estimation of conditional quantiles of a nonlinear time series model is formulated as a nonsmooth optimization problem involving an asymmetric loss function. This asymmetric loss function is nonsmooth and is of the same structure as the so-called 'lopsided' absolute value function. Using an effective smoothing approximation method introduced for this lopsided absolute value function, we obtain a sequence of approximate smooth optimization problems. Some important convergence properties of the approximation are established. Each of these smooth approximate optimization problems is solved by an optimization algorithm based on a sequential quadratic programming approximation with active set strategy. Within the framework of locally linear conditional quantiles, the proposed approach is compared with three other approaches, namely, an approach proposed by Yao and Tong (1996), the Iteratively Reweighted Least Squares method and the Interior-Point method, through some empirical numerical studies using simulated data and the classic lynx pelt series. In particular, the empirical performance of the proposed approach is almost identical with that of the Interior-Point method, both methods being slightly better than the Iteratively Reweighted Least Squares method. The Yao-Tong approach is comparable with the other methods in the ideal cases for the Yao-Tong method, but otherwise it is outperformed by other approaches. An important merit of the proposed approach is that it is conceptually simple and can be readily applied to parametrically nonlinear conditional quantile estimation.
Details
- Title: Subtitle
- Estimation of conditional quantiles by a new smoothing approximation of asymmetric loss functions
- Creators
- G H Zhao - Aff1 Aff2K L Teo - Hong Kong Polytechnic UniversityK S Chan - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Statistics and computing, Vol.15(1), pp.5-11
- Publisher
- SPRINGER
- DOI
- 10.1007/s11222-005-4785-9
- ISSN
- 0960-3174
- eISSN
- 1573-1375
- Number of pages
- 7
- Language
- English
- Date published
- 01/01/2005
- Academic Unit
- Statistics and Actuarial Science; Radiology
- Record Identifier
- 9984257733402771
Metrics
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