Least Weighted Absolute Value Estimator with an Application to Investment Data

0535711 - ÚI 2021 RIV CZ eng C - Konferenční příspěvek (zahraniční konf.)
Vidnerová, Petra - Kalina, Jan
Least Weighted Absolute Value Estimator with an Application to Investment Data.
The 14th International Days of Statistics and Economics Conference Proceedings. Slaný: Melandrium, 2020 - (Löster, T.; Pavelka, T.), s. 1357-1366. ISBN 978-80-87990-22-3.
[International Days of Statistics and Economics /14./. Prague (CZ), 10.09.2020-12.09.2020]
Grant CEP: GA ČR(CZ) GA18-23827S; GA ČR(CZ) GA19-05704S
Institucionální podpora: RVO:67985807
Klíčová slova: robust regression * regression median * implicit weighting * computational aspects * nonparametric bootstrap
Obor OECD: Statistics and probability
https://msed.vse.cz/msed_2020/article/351-Vidnerova-Petra-paper.pdf

While linear regression represents the most fundamental model in current econometrics, the least squares (LS) estimator of its parameters is notoriously known to be vulnerable to the presence of outlying measurements (outliers) in the data. The class of M-estimators, thoroughly investigated since the groundbreaking work by Huber in 1960s, belongs to the classical robust estimation methodology (Jurečková et al., 2019). M-estimators are nevertheless not robust with respect to leverage points, which are defined as values outlying on the horizontal axis (i.e. outlying in one or more regressors). The least trimmed squares estimator seems therefore a more suitable highly robust method, i.e. with a high breakdown point (Rousseeuw & Leroy, 1987). Its version with weights implicitly assigned to individual observations, denoted as the least weighted squares estimator, was proposed and investigated in Víšek (2011). A trimmed estimator based on the 𝐿1-norm is available as the least trimmed absolute value estimator (Hawkins & Olive, 1999), which has not however acquired attention of practical econometricians. Moreover, to the best of our knowledge, its version with weights implicitly assigned to individual observations seems to be still lacking.
Trvalý link: http://hdl.handle.net/11104/0313658