Asymptotic Properties Of Functional Nonparametric And Semi-parametric Regression Model Estimation With Responses Missing At Random

As we know that functional regression model is one of the most important statistics models in FDA,which is employed to explore the relationship between a scalar response variable and a functional explanatory variable.Functional nonparametric regression is the one of the commonly model.So that solve the “curse of dimensionality” in nonparametric regression,produce a scalar response variable is explained by the sum of an unknown linear model and an unknown functional nonparametric,that is semi-functional partial linear regression model.But in practical work such as sampling survey,pharmaceutical tracing test,reliability test and so on,data are often observed incompletely,for instance,responses being missing at random(MAR),so the problem for statistics models in MAR is significant to study.So in this paper,we construct the estimation of functional nonparametric regression model and semi-functional partially linear regression model with responses missing at random.And investigate asymptotic properties of estimators.Finally,a simulation study shows the usefulness of the proposed methodology.The details are given as follow:(1)This section focuses on nonparametric regression model,where a scalar response variable Y with missing at random(MAR)given a random variable X taking values in a semi-metric abstract space H.The main aim of this work is to investigate nonparametric kernel estimators of nonparametric models and prove the uniform almost complete convergence under MAR.These uniform consistency result are(or will be)key tools for many cases of missing data in functional data analysis.(2)This sectionfocuses on semi-functional partially linear regression model,where a scalar response variable with missing at random(MAR)is explained by the sum of an unknown linear combination of the components of multivariate random variables and an unknown transformation of a functional random variable.The main work of this section is to construct the estimators of unknown parametric and unknown regression operator,and then investigate some asymptotic properties of the estima-tors such as almost sure convergence with rates of the nonparametric component and asymptotic distribution of the parametric one respectively for the responses MAR.Then,a simulation study is carried out to illustrate the finite sample performances of the estimators.Finally,an application to real data analysis for food fat predictions shows the usefulness of the proposed methodology.