TY - JOUR

T1 - Convergence of the huber regression m-estimate in the presence of dense outliers

AU - Tsakonas, Efthymios

AU - Jalden, Joakim

AU - Sidiropoulos, Nicholas D.

AU - Ottersten, Bjorn

PY - 2014/10

Y1 - 2014/10

N2 - We consider the problem of estimating a deterministic unknown vector which depends linearly on n noisy measurements, additionally contaminated with (possibly unbounded) additive outliers. The measurement matrix of the model (i.e., the matrix involved in the linear transformation of the sought vector) is assumed known, and comprised of standard Gaussian i.i.d. entries. The outlier variables are assumed independent of the measurement matrix, deterministic or random with possibly unknown distribution. Under these assumptions we provide a simple proof that the minimizer of the Huber penalty function of the residuals converges to the true parameter vector with a n -rate, even when outliers are dense, in the sense that there is a constant linear fraction of contaminated measurements which can be arbitrarily close to one. The constants influencing the rate of convergence are shown to explicitly depend on the outlier contamination level.

AB - We consider the problem of estimating a deterministic unknown vector which depends linearly on n noisy measurements, additionally contaminated with (possibly unbounded) additive outliers. The measurement matrix of the model (i.e., the matrix involved in the linear transformation of the sought vector) is assumed known, and comprised of standard Gaussian i.i.d. entries. The outlier variables are assumed independent of the measurement matrix, deterministic or random with possibly unknown distribution. Under these assumptions we provide a simple proof that the minimizer of the Huber penalty function of the residuals converges to the true parameter vector with a n -rate, even when outliers are dense, in the sense that there is a constant linear fraction of contaminated measurements which can be arbitrarily close to one. The constants influencing the rate of convergence are shown to explicitly depend on the outlier contamination level.

KW - Breakdown point (BP)

KW - Huber estimator

KW - dense outliers

KW - performance analysis

UR - http://www.scopus.com/inward/record.url?scp=84903291685&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84903291685&partnerID=8YFLogxK

U2 - 10.1109/LSP.2014.2329811

DO - 10.1109/LSP.2014.2329811

M3 - Article

AN - SCOPUS:84903291685

SN - 1070-9908

VL - 21

SP - 1211

EP - 1214

JO - IEEE Signal Processing Letters

JF - IEEE Signal Processing Letters

IS - 10

M1 - 6828704

ER -