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

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

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.

Suggested Citation

  • Pan, Yan & Duan, Fabing & Xu, Liyan & Chapeau-Blondeau, François, 2019. "Benefits of noise in M-estimators: Optimal noise level and probability density," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    • Handle: RePEc:eee:phsmap:v:534:y:2019:i:c:s0378437119304224
    DOI: 10.1016/j.physa.2019.04.071
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    Cited by:

    1. Yang, Ting & Liu, Shujun & Liu, Hongqing & Zhang, Kui & Guo, Zhiwei & Yang, Shiju & Li, Yu, 2023. "Stochastic resonance in Bayesian estimation and CRLB for nonlinear system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).

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