{"title":"An unbiased estimator of the causal effect on the variance based on the back-door criterion in Gaussian linear structural equation models","authors":"Taiki Tezuka, Manabu Kuroki","doi":"10.1016/j.jmva.2023.105201","DOIUrl":null,"url":null,"abstract":"<div><p>This paper assumes a context in which cause–effect relationships between random variables can be represented by a Gaussian linear structural equation model<span> and the corresponding directed acyclic graph. We consider the situation where we observe a set of random variables satisfying the so-called back-door criterion. When the ordinary least squares method is utilized to estimate the total effect, we formulate the unbiased estimator<span> of the causal effect (the estimated causal effect) on the variance of the outcome variable with external intervention in which a treatment variable is set to a specified constant value. In addition, we provide the variance formula for the estimated causal effect on the variance. The variance formula proposed in this paper is exact, in contrast to those in most previous studies on estimating causal effects.</span></span></p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"197 ","pages":"Article 105201"},"PeriodicalIF":1.4000,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Multivariate Analysis","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0047259X23000477","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
Abstract
This paper assumes a context in which cause–effect relationships between random variables can be represented by a Gaussian linear structural equation model and the corresponding directed acyclic graph. We consider the situation where we observe a set of random variables satisfying the so-called back-door criterion. When the ordinary least squares method is utilized to estimate the total effect, we formulate the unbiased estimator of the causal effect (the estimated causal effect) on the variance of the outcome variable with external intervention in which a treatment variable is set to a specified constant value. In addition, we provide the variance formula for the estimated causal effect on the variance. The variance formula proposed in this paper is exact, in contrast to those in most previous studies on estimating causal effects.
期刊介绍:
Founded in 1971, the Journal of Multivariate Analysis (JMVA) is the central venue for the publication of new, relevant methodology and particularly innovative applications pertaining to the analysis and interpretation of multidimensional data.
The journal welcomes contributions to all aspects of multivariate data analysis and modeling, including cluster analysis, discriminant analysis, factor analysis, and multidimensional continuous or discrete distribution theory. Topics of current interest include, but are not limited to, inferential aspects of
Copula modeling
Functional data analysis
Graphical modeling
High-dimensional data analysis
Image analysis
Multivariate extreme-value theory
Sparse modeling
Spatial statistics.