On the identification of random variables from quantized observations

TL;DR

This paper demonstrates that scale and shift parameters of certain probability distributions can be identified from quantized data, and confirms the consistency of maximum likelihood estimation for quantized Gaussian autoregressive models.

Contribution

It provides theoretical proof for parameter identifiability from quantized observations and establishes the consistency of MLE in quantized Gaussian AR processes.

Findings

Parameters can be identified from quantized data under certain conditions.

MLE is consistent for quantized Gaussian autoregressive models.

Theoretical framework supports parameter estimation from coarse data.

Abstract

We prove that the scale and shift parameters of a family of probability laws can be identified from quantized values, under appropriate assumptions. As an application, we show the consistency of the maximum likelihood estimator for the parameters of a quantized Gaussian autoregressive process.