Layman’s abstract: Linear mode regression with covariate measurement error

Every few days, we will be publishing layman’s abstracts of new articles from our prestigious portfolio of journals in statistics. The aim is to highlight the latest research to a broader audience in an accessible format.

The article featured today is from The Canadian Journal of Statistics: ‘Linear mode regression with covariate measurement error’ by Xiang Li and Xianzheng Huang, published in issue 47:2, pp 262-280.

thumbnail image: Layman's abstract: Linear mode regression with covariate measurement error

In this article, the authors consider the problem of estimating the mode of a response conditioning on a covariate while assuming a linear function in the covariate for the mode. Moreover, in their study, the covariate cannot be measured precisely due to error contamination, and the distribution of the response given the covariate is left unspecified. Based on an existing method that solves a similar problem but with covariates measured precisely, the authors develop two approaches to revise the existing method in order to account for covariate measurement error when drawing inference on the mode model. The first method exploits a simulation-based approach to produce consistent estimators for the parameters in the linear mode model. In the second method, the authors adopt strategies in nonparametric density estimation in the presence of measurement error to construct an objective function, of which the maximizer yields consistent estimators for these parameters. Through rigorous asymptotic analyses of estimators resulting from the second method, the authors establish asymptotic normality for them.

Image copyright:
 Patrick Rhodes