Error variance estimation in semi-functional partially linear regression models

Germán Aneiros, Nengxiang Ling and Philippe Vieu

Journal of Nonparametric Statistics, 2015, vol. 27, issue 3, 316-330

Abstract: This paper focuses on partially linear regression models with several real and functional covariates. The aim is to construct an estimate of the variance of the error. In our model, a real-valued response variable is explained by the sum of an unknown linear combination of the components of a multivariate random variable and an unknown transformation of a functional random variable, and the second sample moment based on residuals from a semiparametric fit is proposed for estimating the error variance. Then, the asymptotic normality and the law of the iterated logarithm of such estimator are obtained. Finally, a simulation study illustrates the finite sample behaviour of the estimator, while an application to real data shows the usefulness of the proposed methodology, more specifically for confidence region construction.

Date: 2015
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DOI: 10.1080/10485252.2015.1042376

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