Likelihood Estimation with Incomplete Array Variate Observations

TL;DR

This paper introduces methods for estimating parameters of array variate normal models from incomplete high-dimensional array data, enabling better missing data imputation and covariance estimation.

Contribution

It proposes novel estimation techniques for array variate models with missing data, including a semi-parametric mixed effects model and an efficient estimation algorithm.

Findings

Effective missing data imputation demonstrated.

Accurate estimation of mean and covariance parameters.

Validated methods with simulations and genetics data.

Abstract

Missing data is an important challenge when dealing with high dimensional data arranged in the form of an array. In this paper, we propose methods for estimation of the parameters of array variate normal probability model from partially observed multiway data. The methods developed here are useful for missing data imputation, estimation of mean and covariance parameters for multiway data. A multiway semi-parametric mixed effects model that allows separation of multiway covariance effects is also defined and an efficient algorithm for estimation is recommended. We provide simulation results along with real life data from genetics to demonstrate these methods.