Goodness-of-fit testing for the partially linear model

Abstract

In this paper, we propose a test to assess the relevance of using a partially linear model (PLM).
Constructing our test statistic requires estimating the error variance in the context of a partially linear model. For this purpose, we use specific estimators of error variance. The test statistic is based on the difference between two such estimators. This difference is expected to be close to zero under the null hypothesis H0 and significantly larger under the alternative hypothesis H1. We establish the asymptotic properties of the proposed test statistic, and through simulations on finite-sample data, we evaluate its performance.