Nonparametric Bootstrap Techniques for Implicitly Weighted Robust Estimators

0497296 - ÚI 2019 RIV CZ eng C - Conference Paper (international conference)
Kalina, Jan
Nonparametric Bootstrap Techniques for Implicitly Weighted Robust Estimators.
The 12th International Days of Statistics and Economics Conference Proceedings. Slaný: Melandrium, 2018 - (Löster, T.; Pavelka, T.), s. 770-779. ISBN 978-80-87990-14-8.
[International Days of Statistics and Economics /12./. Prague (CZ), 06.09.2018-08.09.2018]
R&D Projects: GA ČR GA17-07384S
Institutional support: RVO:67985807
Keywords : robust statistics * econometrics * correlation coefficient * multivariate data
OECD category: Statistics and probability
https://msed.vse.cz/msed_2018/article/3-Kalina-Jan-paper.pdf

The paper is devoted to highly robust statistical estimators based on implicit weighting, which have a potential to find econometric applications. Two particular methods include a robust correlation coefficient based on the least weighted squares regression and the minimum weighted covariance determinant estimator, where the latter allows to estimate the mean and covariance matrix of multivariate data. New tools are proposed allowing to test hypotheses about these robust estimators or to estimate their variance. The techniques considered in the paper include resampling approaches with or without replacement, i.e. permutation tests, bootstrap variance estimation, and bootstrap confidence intervals. The performance of the newly described tools is illustrated on numerical examples. They reveal the suitability of the robust procedures also for non-contaminated data, as their confidence intervals are not much wider compared to those for standard maximum likelihood estimators. While resampling without replacement turns out to be more suitable for hypothesis testing, bootstrapping with replacement yields reliable confidence intervals but not corresponding hypothesis tests.
Permanent Link: http://hdl.handle.net/11104/0289872