### Abstract

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 Portnoy and Koenker^{[28]}. 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.

Original language | English (US) |
---|---|

Pages (from-to) | 225-236 |

Number of pages | 12 |

Journal | Acta Mathematicae Applicatae Sinica |

Volume | 21 |

Issue number | 2 |

DOIs | |

State | Published - May 2005 |

### Fingerprint

### Keywords

- Interior-point algorithm
- Quantile regression
- Sparse linear algebra

### ASJC Scopus subject areas

- Applied Mathematics

### Cite this

*Acta Mathematicae Applicatae Sinica*,

*21*(2), 225-236. https://doi.org/10.1007/s10255-005-0231-1

**A frisch-newton algorithm for sparse quantile regression.** / Koenker, Roger; Ng, Pin T.

Research output: Contribution to journal › Article

*Acta Mathematicae Applicatae Sinica*, vol. 21, no. 2, pp. 225-236. https://doi.org/10.1007/s10255-005-0231-1

}

TY - JOUR

T1 - A frisch-newton algorithm for sparse quantile regression

AU - Koenker, Roger

AU - Ng, Pin T

PY - 2005/5

Y1 - 2005/5

N2 - 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 Portnoy and Koenker[28]. 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.

AB - 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 Portnoy and Koenker[28]. 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.

KW - Interior-point algorithm

KW - Quantile regression

KW - Sparse linear algebra

UR - http://www.scopus.com/inward/record.url?scp=18244365578&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=18244365578&partnerID=8YFLogxK

U2 - 10.1007/s10255-005-0231-1

DO - 10.1007/s10255-005-0231-1

M3 - Article

AN - SCOPUS:18244365578

VL - 21

SP - 225

EP - 236

JO - Acta Mathematicae Applicatae Sinica

JF - Acta Mathematicae Applicatae Sinica

SN - 0168-9673

IS - 2

ER -