On Parameter Estimation for Cusp-type Signals

TL;DR

This paper investigates the asymptotic behavior of maximum likelihood and Bayesian estimators for cusp-type signals in white Gaussian noise, including cases of model misspecification where the true signal is smooth.

Contribution

It provides new insights into the estimation rates and distributions when signals have cusp singularities and addresses the impact of misspecification of the signal's regularity.

Findings

Characterizes the asymptotic distribution of estimators for cusp signals.

Analyzes the effect of misspecification on estimation rates.

Describes the properties of estimators in small noise asymptotics.

Abstract

We consider the problem of parameter estimation by the observations of deterministic signal in white gaussian noise. It is supposed that the signal has a singularity of cusp-type. The properties of the maximum likelihood and bayesian estimators are described in the asymptotics of small noise. Special attention is paid to the problem of parameter estimation in the situation of misspecification in regularity, i.e.; the statistician supposes that the observed signal has this singularity, but the real signal is smooth. The rate and the asymptotic distribution of the maximum likelihood estimator in this situation are described.