Semiparametric Robust Estimation of Population Location

TL;DR

This paper introduces a semiparametric method for robustly estimating the main signal in noisy data, combining parametric modeling of the signal with a nonparametric background, and employs an FFT-accelerated algorithm for efficiency.

Contribution

It proposes a novel semiparametric approach that models only the dominant component parametrically, improving robustness and scalability over traditional methods.

Findings

Achieves significant speedups with FFT-accelerated likelihood maximization.

Maintains statistical accuracy and robustness in large samples.

Outperforms vanilla weighted EM in computational efficiency.

Abstract

Real-world measurements often comprise a dominant signal contaminated by a noisy background. Robustly estimating the dominant signal in practice has been a fundamental statistical problem. Classically, mixture models have been used to cluster the heterogeneous population into homogeneous components. Modeling such data with fully parametric models risks bias under misspecification, while fully nonparametric approaches can dissipate power and computational resources. We propose a middle path: a semiparametric method that models only the dominant component parametrically and leaves the background completely nonparametric, yet remains computationally scalable and statistically robust. So instead of outlier downweighting, traditionally done in robust statistics literature, we maximize the observed likelihood such that the noisy background is absorbed by the nonparametric component. Computationally, we propose a new approximate FFT-accelerated likelihood maximization algorithm. Empirically, this FFT plug-in achieves order-of-magnitude speedups over vanilla weighted EM while preserving statistical accuracy and large sample properties.