Sensitivity analysis of constrained linear L1 regression: Perturbations to constraints, addition and deletion of observations

M.A. Lukas; M. Shi

doi:10.1016/j.csda.2004.04.014

Back

Sensitivity analysis of constrained linear L1 regression: Perturbations to constraints, addition and deletion of observations

Journal article

Open access

Peer reviewed

Sensitivity analysis of constrained linear L1 regression: Perturbations to constraints, addition and deletion of observations

M.A. Lukas and M. Shi

Computational Statistics and Data Analysis, Vol.51(2), pp.1213-1231

15/11/2006

DOI: https://doi.org/10.1016/j.csda.2004.04.014

Files and links (2)

pdf

sensitivity_analysis-perturbations_to_constraints.pdfDownload View

Author’s Version Open Access

url

Link to Published Version *Subscription may be requiredView

Abstract

This paper extends the direct sensitivity analysis of Shi and Lukas [2005, Sensitivity analysis of constrained linear L 1 regression: perturbations to response and predictor variables. Comput. Statist. Data Anal. 48, 779-802] of linear L 1 (least absolute deviations) regression with linear equality and inequality constraints on the parameters. Using the same active set framework of the reduced gradient algorithm (RGA), we investigate the effect on the L 1 regression estimate of small perturbations to the constraints (constants and coefficients). It is shown that the constrained estimate is stable, but not uniformly stable, and in certain cases it is unchanged. We also consider the effect of addition and deletion of observations and determine conditions under which the estimate is unchanged. The results demonstrate the robustness of L 1 regression and provide useful diagnostic information about the influence of observations. Results characterizing the (possibly non-unique) solution set are also given. The sensitivity results are illustrated with numerical simulations on the problem of derivative estimation under a concavity constraint.

Details

Title: Sensitivity analysis of constrained linear L1 regression: Perturbations to constraints, addition and deletion of observations
Authors/Creators: M.A. Lukas (Author/Creator)
M. Shi (Author/Creator)
Publication Details: Computational Statistics and Data Analysis, Vol.51(2), pp.1213-1231
Publisher: Elsevier
Identifiers: 991005544938807891
Copyright: © 2006 Elsevier B.V.
Murdoch Affiliation: School of Chemical and Mathematical Science
Language: English
Resource Type: Journal article

UN Sustainable Development Goals (SDGs)

This output has contributed to the advancement of the following goals:

Source: InCites

Metrics

161 File views/ downloads

87 Record Views

1 Times Cited - Web of Science

InCites Highlights

These are selected metrics from InCites Benchmarking & Analytics tool, related to this output

Collaboration types: Domestic collaboration
Citation topics: 9 Mathematics; 9.92 Statistical Methods; 9.92.220 Robust Estimation
Web Of Science research areas: Computer Science, Interdisciplinary Applications; Statistics & Probability
ESI research areas: Mathematics