Simultaneous Confidence Bands For Nonparametric Regression Model With Deterministic Design And Functional Data With Holiday Effects

In this dissertation,motivated by strata pressure data and weekly sporting goods sales data,we study nonparametric regression model with deterministic design and functional data with holiday effects.Oracally efficient estimation and the corresponding simultaneous confidence bands(SCBs)are proposed in these modelsFirst,for the deterministic design nonparametric regression model,asymptotical-ly correct SCBs are proposed for the mean and variance functions by using kernel smoothing and two-step spline-kernel regression,respectively.The variance estimation is as efficient up to order n-1/2 as an infeasible estimator if the mean function were known.Simulation experiments provide strong evidence that corroborates the asymp-totic theory.The proposed SCBs are used to analyze two sets of strata pressure from the Bullianta Coal Mine in Erdos City,Inner Mongolia,ChinaSecond,functional data with holiday effects model refers to the case where the functional data has spikes in mean.It is proposed in the analysis of weekly sport-ing goods sales data.For such functional data,two step estimation procedures are formulated for the population mean function and holiday effect parameters,which cor-respond to the population sales curve and the spikes in sales during holiday times.The estimators are based on spline smoothing for individual trajectories using non holiday observations,and are shown to be oracally efficient in the sense that both the mean function and holiday effects are estimated as efficiently as if all individual trajectories were known a priori.Consequently,asymptotic SCBs and confidence intervals(CIs)are established for the mean function and holiday effects,respectively.Two sample ex-tensions are also formulated and simulation experiments provide strong evidence that corroborates the asymptotic theory.Application to sporting goods sales data has led to a number of new discoveries.