Frequency Domain Empirical Likelihood Using Distributional Constraint.

Music City Center 

This work introduces a framework for robust Bayesian inference by integrating
two methodologies: a Bayesian exponentially tilted empirical likelihood and a
frequency domain empirical likelihood, each designed to address different aspects
of statistical modeling. The first component leverages a new variant of
the Wasserstein metric to concentrate the likelihood near a chosen parametric
family, enabling robust inference on model parameters in the presence of outliers.
We extend this idea to dependent data through a data transformation
(i.e., a Fourier transform) developed in terms of the spectral distribution. In
this semi-parametric approach, instead of using moment-based constraints as in
the existing literature, we employ distributional constraints so that the distribution
is concentrated around a guessed parametric family. Applications extend
to robust inference, spectral analysis, Whittle estimation, and goodness-of-fit
testing, with implications for trustworthy machine learning.

Frequency Domain Empirical Likelihood

Robust Inference

Whittle Estimation

Spectral Distribution

Periodograms 

Section on Statistics and the Environment