Nonparametric Kernel Regression Estimation For Functional Stationary Ergodic Data With Missing At Random

In recent years, with the development of science and technology and the computer is widely used. Data acquisition techniques and methods emerge in endlessly, and more and more fields of observed data have the characteristics of function type. And so, makes the theoretical properties of functional data research become one of hotspots in the current statistics. But in many practical problems, because of human or other unknown factors, it is easy to tend to get a large number of missing data. For instance, in drug tracking, survival analysis, reliability life test and social economic research and so on, the missing data is widespread in these research fields. So, to study the statistical properties of functional missing data has a very important practical significance and its results of the study gradually by the attention of the scholars.In this dissertation, we mainly study some asymptotic properties of nonparametric kernel regression estimation for functional stationary ergodic data with missing at random, and we obtain some better statistical results of the samples. The details are given as follows:Firstly, based on the missing at random(MAR) mechanism, make the use of the famous N-W estimates, we obtain the convergence in probability, asymptotic normality of the estimator of the nonparametric regression estimation model for functional stationary ergodic data.Secondly, by the asymptotic normality we obtain some lemmas and the asymptotic (1-α) confidence interval for the regression function operator is also presented.Thirdly, at the end of the article we are given a simulation study of the nonparametric estimates of functional data, we compared the estimator of the mean square error for different loss rates under the missing date; we obtain the good satisfactory results of the estimation.