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A sparse implementation of the Frisch-Newton algorithm for 1uantile regression: Working paper series--03-03

Koenker, Roger and Ng, Pin (2003) A sparse implementation of the Frisch-Newton algorithm for 1uantile regression: Working paper series--03-03. Working Paper. NAU W.A. Franke College of Business.


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Recent experience has shown that interior-point methods using a log barrier approach are far superior to classical simplex methods for computing solutions to large parametric quantile regression problems. In many large empirical applications, the design matrix has a very sparse structure. A typical example is the classical fixed-effect model for panel data where the parametric dimension of the model can be quite large, but the number of non-zero elements is quite small. Adopting recent developments in sparse linear algebra we introduce a modified version of the Frisch-Newton algorithm for quantile regression described in Koenker and Portnoy (1997). The new algorithm substantially reduces the storage (memory) requirements and increases computational speed. The modified algorithm also facilitates the development of nonparametric quantile regression methods. The pseudo design matrices employed in nonparametric quantile regression smoothing are inherently sparse in both the fidelity and roughness penalty components. Exploiting the sparse structure of these problems opens up a whole range of new possibilities for multivariate smoothing on large data sets via ANOVA-type decomposition and partial linear models.

Item Type: Monograph (Working Paper)
Publisher’s Statement: Copyright, where appropriate, is held by the author.
ID number or DOI: 03-03
Keywords: Working paper, Frisch-Newton Algorithm, Quantile Regression
Subjects: H Social Sciences > HA Statistics
Q Science > QA Mathematics
NAU Depositing Author Academic Status: Faculty/Staff
Department/Unit: The W.A. Franke College of Business
Date Deposited: 19 Oct 2015 23:50
URI: http://openknowledge.nau.edu/id/eprint/1599

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