@inproceedings{df28b916087a4402a9066172b776f87e,
title = "Lfinite Sample Bounds on the Performance of Weighted Linear Least Squares in Sub-Gaussian Correlated Noise",
abstract = "In this paper we provide finite sample bounds on the performance of the weighted linear least squares estimator in sub-Gaussian martingale difference correlated noise. In contrast to standard performance analysis which uses bounds on the mean square error together with asymptotic normality, our bounds are based on concentration of measure. We extend previous results by analyzing the weighted least squares estimator and provide novel results in the case of correlated noise and heteroscedasticity. Using these bounds we obtain accurate bounds on the tail of the estimator. We show fast exponential convergence of the L∞ probability of error. We analyze the fixed design setting. We use the results to analyze the performance of the weighted least squares estimator for the important problem of system identification. We show how to extend the results to different norms and state a theorem for the L2 norm.",
keywords = "Estimation, concentration bounds, confidence bounds, finite sample, large deviations, martingale difference sequence, non Gaussian, system identification, weighted least squares",
author = "Michael Krikheli and Amir Leshem",
note = "Publisher Copyright: {\textcopyright} 2019 IEEE.; 2019 IEEE Data Science Workshop, DSW 2019 ; Conference date: 02-06-2019 Through 05-06-2019",
year = "2019",
month = jun,
doi = "10.1109/dsw.2019.8755574",
language = "الإنجليزيّة",
series = "2019 IEEE Data Science Workshop, DSW 2019 - Proceedings",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "110--114",
booktitle = "2019 IEEE Data Science Workshop, DSW 2019 - Proceedings",
address = "الولايات المتّحدة",
}