Estimations of Means and Variances in a Markov Linear Model

Gutierrez Abraham () and Müller Sebastian ()
Additional contact information
Gutierrez Abraham: Institute of Discrete Mathematics, Graz University of Technology, Graz, Austria
Müller Sebastian: I2M – UMR 7373, Aix-Marseille Université, CNRS, Centrale Marseille, Marseille, France

Stochastics and Quality Control, 2022, vol. 37, issue 1, 21-43

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.

Keywords: Linear Model; Multicollinearity; Regression; Markov Chain; Directed Acyclic Graph; Multi-dimensional Anscombe Theorem (search for similar items in EconPapers)
Date: 2022
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1515/eqc-2022-0004 (text/html)
For access to full text, subscription to the journal or payment for the individual article is required.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bpj:ecqcon:v:37:y:2022:i:1:p:21-43:n:1

Ordering information: This journal article can be ordered from
https://www.degruyter.com/journal/key/eqc/html

DOI: 10.1515/eqc-2022-0004

Access Statistics for this article

Stochastics and Quality Control is currently edited by George P. Yanev

More articles in Stochastics and Quality Control from De Gruyter
Bibliographic data for series maintained by Peter Golla ().