Semi-parametric second-order efficient estimation of the period of a signal

TL;DR

This paper develops a semi-parametric approach for estimating the period of a periodic signal in Gaussian noise, providing second-order efficiency and optimality results for the proposed estimators.

Contribution

It introduces a penalized maximum likelihood estimator for the period and establishes its second-order efficiency in a semi-parametric setting.

Findings

The estimator achieves second-order asymptotic optimality.

A minimax problem for the second-order term is formulated and solved.

The proposed method outperforms existing estimators in terms of risk.

Abstract

This paper is concerned with the estimation of the period of an unknown periodic function in Gaussian white noise. A class of estimators of the period is constructed by means of a penalized maximum likelihood method. A second-order asymptotic expansion of the risk of these estimators is obtained. Moreover, the minimax problem for the second-order term is studied and an estimator of the preceding class is shown to be second order efficient.