Estimation For Semi-functional Linear Model With Error In Variables

With the rapid development of science and technology,people collect more and more complex data,so the concept of functional data also appears,because the functional data in many scientific fields are widely used,functional data analysis(FDA)has attracted more and more attention of scholars.However,in practical problems,the sample data is often collected with the measurement error,so the regression analysis with measurement error has also been rapid development over the past few decades.This paper studies estimation in semi-functional linear regression when function and real-valued random variables are both measured with additive error.By means of function-al principal component analysis and kernel smoothing techniques,we obtain the estimator of the slope function of function-valued variable and the estimator of nonparametric com-ponent.To account for errors in covariate,deconvolution is involved in the construction of a new class of kernel estimator.The consistency and convergence rates of the estima-tors of unknown slope function and nonparametric component are established under some suitable conditions.we also illustrate the finite sample performance of our methods with some simulations.