Benefits of noise in M-estimators: Optimal noise level and probability density

Yan Pan, Fabing Duan, Liyan Xu and François Chapeau-Blondeau

Physica A: Statistical Mechanics and its Applications, 2019, vol. 534, issue C

Abstract: For the robust estimation of a location parameter, we consider a parallel array of maximum likelihood type estimators (M-estimators). We investigate the possibility of added noise as a design variable of the M-estimators, and characterize a nonzero optimal amount of added noise maximizing the efficiency for estimation. The added noise shows its benefits to the asymptotic efficiency of the M-estimator when the noise level and the noise probability density are optimally tuned. The optimal noise level can be theoretically derived by maximizing the asymptotic efficiency as the probability density of added noise is given. Based on the Parzen-window density estimation technique, we approximate the infinite-dimensional non-convex optimization of the optimal probability density of added noise as a simpler optimization problem with respect to a finite-dimensional vector under certain constraints. This approximate solution for the optimal probability density of added noise shows its feasibility for various M-estimators with an arbitrary array size, which is also validated by simulation results.

Keywords: Noise benefit; Asymptotic efficiency; M-estimator; Optimal noise probability density; Parzen-window estimation (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437119304224
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:534:y:2019:i:c:s0378437119304224

DOI: 10.1016/j.physa.2019.04.071

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().