A fast and efficient implementation of qualitatively constrained quantile smoothing splines

Pin T Ng, Martin Maechler

Research output: Contribution to journalArticle

37 Citations (Scopus)

Abstract

We implement a fast and efficient algorithm to compute qualitatively constrained smoothing and regression splines for quantile regression, exploiting the sparse structure of the design matrices involved in the method. In a previous implementation, the linear program involved was solved using a simplex-like algorithm for quantile smoothing splines. The current implementation uses the Frisch-Newton algorithm, recently escribed by Koenker and Ng (2005b). It is a variant of the interior-point algorithm proposed by Portnoy and Koenker (1997), which has been shown to outperform the simplex method in many applications. The current R implementation relies on the R package SparseM of Koenker and Ng (2003) which contains a collection of basic linear algebra routines for sparse matrices to exploit the sparse structure of the matrices involved in the linear program to further speed up computation and save memory usage. A small simulation illustrates the superior performance of the new implementation.

Original languageEnglish (US)
Pages (from-to)315-328
Number of pages14
JournalStatistical Modelling
Volume7
Issue number4
DOIs
StatePublished - Dec 2007

Fingerprint

Smoothing Splines
Quantile
Efficient Implementation
Linear Program
Regression Splines
Interior-point Algorithm
Quantile Regression
Simplex Method
Sparse matrix
Linear algebra
Fast Algorithm
Speedup
Efficient Algorithms
Smoothing splines
Simulation
Linear program

Keywords

  • Interior-point
  • Linear program
  • Nonparametric regression
  • Quantile regression
  • Simplex
  • Smoothing spline

ASJC Scopus subject areas

  • Statistics and Probability

Cite this

A fast and efficient implementation of qualitatively constrained quantile smoothing splines. / Ng, Pin T; Maechler, Martin.

In: Statistical Modelling, Vol. 7, No. 4, 12.2007, p. 315-328.

Research output: Contribution to journalArticle

@article{99e1d29483504bc7909e011ec195400f,
title = "A fast and efficient implementation of qualitatively constrained quantile smoothing splines",
abstract = "We implement a fast and efficient algorithm to compute qualitatively constrained smoothing and regression splines for quantile regression, exploiting the sparse structure of the design matrices involved in the method. In a previous implementation, the linear program involved was solved using a simplex-like algorithm for quantile smoothing splines. The current implementation uses the Frisch-Newton algorithm, recently escribed by Koenker and Ng (2005b). It is a variant of the interior-point algorithm proposed by Portnoy and Koenker (1997), which has been shown to outperform the simplex method in many applications. The current R implementation relies on the R package SparseM of Koenker and Ng (2003) which contains a collection of basic linear algebra routines for sparse matrices to exploit the sparse structure of the matrices involved in the linear program to further speed up computation and save memory usage. A small simulation illustrates the superior performance of the new implementation.",
keywords = "Interior-point, Linear program, Nonparametric regression, Quantile regression, Simplex, Smoothing spline",
author = "Ng, {Pin T} and Martin Maechler",
year = "2007",
month = "12",
doi = "10.1177/1471082X0700700403",
language = "English (US)",
volume = "7",
pages = "315--328",
journal = "Statistical Modelling",
issn = "1471-082X",
publisher = "SAGE Publications Ltd",
number = "4",

}

TY - JOUR

T1 - A fast and efficient implementation of qualitatively constrained quantile smoothing splines

AU - Ng, Pin T

AU - Maechler, Martin

PY - 2007/12

Y1 - 2007/12

N2 - We implement a fast and efficient algorithm to compute qualitatively constrained smoothing and regression splines for quantile regression, exploiting the sparse structure of the design matrices involved in the method. In a previous implementation, the linear program involved was solved using a simplex-like algorithm for quantile smoothing splines. The current implementation uses the Frisch-Newton algorithm, recently escribed by Koenker and Ng (2005b). It is a variant of the interior-point algorithm proposed by Portnoy and Koenker (1997), which has been shown to outperform the simplex method in many applications. The current R implementation relies on the R package SparseM of Koenker and Ng (2003) which contains a collection of basic linear algebra routines for sparse matrices to exploit the sparse structure of the matrices involved in the linear program to further speed up computation and save memory usage. A small simulation illustrates the superior performance of the new implementation.

AB - We implement a fast and efficient algorithm to compute qualitatively constrained smoothing and regression splines for quantile regression, exploiting the sparse structure of the design matrices involved in the method. In a previous implementation, the linear program involved was solved using a simplex-like algorithm for quantile smoothing splines. The current implementation uses the Frisch-Newton algorithm, recently escribed by Koenker and Ng (2005b). It is a variant of the interior-point algorithm proposed by Portnoy and Koenker (1997), which has been shown to outperform the simplex method in many applications. The current R implementation relies on the R package SparseM of Koenker and Ng (2003) which contains a collection of basic linear algebra routines for sparse matrices to exploit the sparse structure of the matrices involved in the linear program to further speed up computation and save memory usage. A small simulation illustrates the superior performance of the new implementation.

KW - Interior-point

KW - Linear program

KW - Nonparametric regression

KW - Quantile regression

KW - Simplex

KW - Smoothing spline

UR - http://www.scopus.com/inward/record.url?scp=45249116756&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=45249116756&partnerID=8YFLogxK

U2 - 10.1177/1471082X0700700403

DO - 10.1177/1471082X0700700403

M3 - Article

AN - SCOPUS:45249116756

VL - 7

SP - 315

EP - 328

JO - Statistical Modelling

JF - Statistical Modelling

SN - 1471-082X

IS - 4

ER -