Soft maximin estimation for heterogeneous data
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Soft maximin estimation for heterogeneous data. / Lund, Adam; Wengel Mogensen, Søren; Richard Hansen, Niels.
In: Scandinavian Journal of Statistics, Vol. 49, No. 4, 2022, p. 1761-1790.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Soft maximin estimation for heterogeneous data
AU - Lund, Adam
AU - Wengel Mogensen, Søren
AU - Richard Hansen, Niels
N1 - Publisher Copyright: © 2022 The Authors. Scandinavian Journal of Statistics published by John Wiley & Sons Ltd on behalf of The Board of the Foundation of the Scandinavian Journal of Statistics.
PY - 2022
Y1 - 2022
N2 - Extracting a common robust signal from data divided into heterogeneous groups is challenging when each group—in addition to the signal—contains large, unique variation components. Previously, maximin estimation was proposed as a robust method in the presence of heterogeneous noise. We propose soft maximin estimation as a computationally attractive alternative aimed at striking a balance between pooled estimation and (hard) maximin estimation. The soft maximin method provides a range of estimators, controlled by a parameter (Formula presented.), that interpolates pooled least squares estimation and maximin estimation. By establishing relevant theoretical properties we argue that the soft maximin method is statistically sensible and computationally attractive. We demonstrate, on real and simulated data, that soft maximin estimation can offer improvements over both pooled OLS and hard maximin in terms of predictive performance and computational complexity. A time and memory efficient implementation is provided in the R package SMME available on CRAN.
AB - Extracting a common robust signal from data divided into heterogeneous groups is challenging when each group—in addition to the signal—contains large, unique variation components. Previously, maximin estimation was proposed as a robust method in the presence of heterogeneous noise. We propose soft maximin estimation as a computationally attractive alternative aimed at striking a balance between pooled estimation and (hard) maximin estimation. The soft maximin method provides a range of estimators, controlled by a parameter (Formula presented.), that interpolates pooled least squares estimation and maximin estimation. By establishing relevant theoretical properties we argue that the soft maximin method is statistically sensible and computationally attractive. We demonstrate, on real and simulated data, that soft maximin estimation can offer improvements over both pooled OLS and hard maximin in terms of predictive performance and computational complexity. A time and memory efficient implementation is provided in the R package SMME available on CRAN.
KW - convex optimization
KW - heterogeneous data
KW - robust estimation
KW - sparse estimation
U2 - 10.1111/sjos.12580
DO - 10.1111/sjos.12580
M3 - Journal article
AN - SCOPUS:85129220199
VL - 49
SP - 1761
EP - 1790
JO - Scandinavian Journal of Statistics
JF - Scandinavian Journal of Statistics
SN - 0303-6898
IS - 4
ER -
ID: 308487811