Statistical Modeling For Two Types Of Complex Data Under Functional Data And Its Application

In the era of big data,data collection methods are constantly innovated and data storage capacity is expanding.A large number of functional data in the form of curves have emerged in the fields of meteorology,biochemistry and neuroimaging.Functional data is continuous functions in time or other dimensions,which brings great challenges to traditional statistical analysis and numerical calculation.However,its infinite dimensional data characteristics can contain more abundant data information,which provides a good opportunity for the development of new statistical theory and broadening the field of practical application.Therefore,functional data analysis has become one of the hot and frontier issues in the field of statistical research.On the other hand,in practical problems,due to the sensitivity of measuring instruments,the errors of measuring personnel,the inability of data observation and other factors,sometimes there are complex situations such as measurement errors or outliers in the data,which makes it difficult for us to directly obtain the true value of the data.Ignoring these complex situations often leads to inaccuracy of modeling and large deviation of parameter estimation.In view of the above analysis,this work mainly focuses on the statistical modeling and application for two kinds of complex data under functional data.The main work is as follows.In Chapter 2,we study the inference for partially functional linear models with distorted measurement error.Based on nonparametric kernel estimation and functional principal component analysis,we use the corrected profile least squares to obtain the estimators of parameter vectors and parameter functions in the model.Under some regular assumptions,the asymptotic properties of the proposed estimator are established.In order to obtain the confidence regions of parameters,firstly,the empirical likelihood method is used to construct confidence interval of the parameters vector in the non-functional linear part,and the asymptotic behavior of the empirical-log-likelihood ratio function is established under some regular assumptions.At the same time,the confidence band of slope function in functional linear part is constructed,which is centered to the estimator of functional principal component analysis.Simulation studies verify the effectiveness of the proposed method.And,the proposed method is applied to China’s real estate data.In Chapter 3,we consider the inference for the single index partial function linear quantile regression models.Based on B-spline basis function,we establish an estimation program to obtain the estimators of unknowns in the model.Under some regular assumptions,the asymptotic properties of the proposed estimators are obtained.At the same time,the effectiveness of the proposed method is verified by simulation and actual data analysis of meat sample dataset.In Chapter 4,we study the inference for functional single index composite quantile regression models.Based on B-spline basis function,we establish an estimation program to obtain the estimators of unknown link function and unknown index function in the model.Under different error distributions,by some simulation results,we can see that the composite quantile regression have stronger robustness.Finally,the proposed method is applied to gasoline NIR spectral dataset.In conclusion,this dissertation is devoted to theory and application of two types of complex data in the field of functional data.The proposed results further enrich the theory and application of functional data.These research results not only have important theoretical value,but also have extensive practical application value.