Estimation on functional partially linear single index measurement error model

In this article, we investigate the functional partially linear single index model when measurement error exists in covariates. The main purpose of this article is to correct the biased estimators caused by additive error and construct the asymptotic properties of unknown parameters and function in model. Asymptotic distribution of the parametric component and the convergence rates of the nonparametric part are obtained under some regularity conditions. Compared with existing literatures in this field, such as functional partially linear and semi-functional partial linear regression model with measurement error, good performance in Tecator data analysis illustrates the advantages of the model and the significance of the proposed methodology. In this process, functional slice inverse regression is applied to estimate the functional single index parameter to improve computational efficiency. Furthermore, a simulation study is also carried out for demonstration.