Estimations of means and variances in a Markov linear model

TL;DR

This paper introduces a novel method for estimating means and variances in multivariate regression with qualitative predictors, using a Markov chain model to account for covariate correlations without assuming homoscedasticity.

Contribution

It proposes a new approach that models covariate correlations with a Markov chain and transforms dependent covariates into independent ones for improved estimation.

Findings

Estimators are asymptotically normally distributed under standard conditions.

Method performs well in simulations and real data applications.

Allows pairwise comparison of covariate contributions.

Abstract

Multivariate regression models and ANOVA are probably the most frequently applied methods of all statistical analyses. We study the case where the predictors are qualitative variables, and the response variable is quantitative. In this case, we propose an alternative to the classic approaches that does not assume homoscedasticity but assumes that a Markov chain can describe the covariates' correlations. This approach transforms the dependent covariates using a change of measure to independent covariates. The transformed estimates allow a pairwise comparison of the mean and variance of the contribution of different values of the covariates. We show that under standard moment conditions, the estimators are asymptotically normally distributed. We test our method with data from simulations and apply it to several classic data sets.