Bit Efficient Toeplitz Covariance Estimation

TL;DR

This paper introduces a new quantized Toeplitz covariance estimator that balances sample size, observed entries, and data resolution, with theoretical guarantees and validated by numerical experiments.

Contribution

We propose a ruler-based quantized Toeplitz covariance estimator with non-asymptotic error bounds and near-optimal convergence rates, addressing data resolution trade-offs.

Findings

Estimator is near-optimal in error bounds

Reducing data resolution has limited impact on accuracy

Numerical experiments validate theoretical results

Abstract

This paper addresses the challenge of Toeplitz covariance matrix estimation from partial entries of random quantized samples. To balance trade-offs among the number of samples, the number of entries observed per sample, and the data resolution, we propose a ruler-based quantized Toeplitz covariance estimator. We derive non-asymptotic error bounds and analyze the convergence rates of the proposed estimator. Our results show that the estimator is near-optimal and imply that reducing data resolution within a certain range has a limited impact on the estimation accuracy. Numerical experiments are provided that validate our theoretical findings and show effectiveness of the proposed estimator.