Parameter Estimation Of Partial Functional Linear Model With Functional Response

With the continuous improvement of modern technology,the form of sample data collected by people in real life has gradually changed from discrete data to functional data.The core idea of functional data analysis is to treat the collected discrete time sample data as elements in a functional space for analysis and processing,so traditional multivariate statistical analysis methods are no longer applicable.At present,research on functional data analysis methods has attracted the attention of scholars at home and abroad,and functional data has increasingly broad application prospects in production practice.In functional data analysis,the functional linear model is an important basis for the inquiry and analysis of functional data.Based on different data forms,a series of basic functional linear models have been proposed to provide a fundamental guarantee for statistical inference research.With the continuous innovation of science and technology,the accuracy and frequency of sample data collection are constantly improving,and the existing models are difficult to solve the problem of more complex data components.Based on this,this dissertation proposes a partial functional linear model with functional response,which expands the scope of application of functional data analysis.This dissertation mainly studies the parameter estimation problem of the partial functional linear model with functional response.Firstly,it introduces the research background and significance of functional data,summarizes the research results in literature in related fields,and outlines the research framework of this article.Secondly,the basic concepts of functional data and functional principal component analysis methods are organized and explained.Next,the partial functional linear model with functional response is defined and explained,and two parameter estimation methods based on single truncation and double truncations are given.Asymptotic properties are given to verify the convergence rates of the estimators.Then,a simulation study is carried out on the estimation of model parameters under finite sample sizes.The simulation results demonstrates the effectiveness and differences of the two estimation methods.Finally,an example analysis is carried out through bicycle rental data to illustrate the practicability of the model and the estimation methods proposed in this dissertation.