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
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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 -