XploRe® — Application Guide

Although many types of confidence bands exist for nonparametric regression with i.i.d. data, theoretical properties of such bands have never been established under dependence. We propose simultaneous confidence bands for nonparametric prediction function of time-series data using spline estimation. Asymptotic properties are established under the assumption of strong mixing, and simulation experiments have provided strong evidence that corroborates with the asymptotic theory. As an application, after removing the environmental Kuznets curve trend effects, the impact of the economic intervention on environmental quality change is quantified for the USA and Japan, with different conclusions.

Section: Simulationmentioning

confidence: 99%

Simultaneous confidence bands for time-series prediction function

Wang¹,

Yang²

2010

“…In this section, we describe how to implement in XploRe (Härdle, Hlávka, and Klinke 2000) the jump points detection procedure by using the results in Theorem 2.1.…”

Section: Methodsmentioning

confidence: 99%

A jump-detecting procedure based on spline estimation

Yang

2011

In a random-design nonparametric regression model, procedures for detecting jumps in the regression function via constant and linear spline estimation method are proposed based on the maximal differences of the spline estimators among neighbouring knots, the limiting distributions of which are obtained when the regression function is smooth. Simulation experiments provide strong evidence that corroborates with the asymptotic theory, while the computing is extremely fast. The detecting procedure is illustrated by analysing the thickness of pennies data set.

“…Our codes are written in XploRe for convenience in order to use kernel smoothing, see [26]. Given any sample {(X i , Y i )} n i=1 from model (1), we use min(X 1 , .…”

Section: Methodsmentioning

confidence: 99%

Spline confidence bands for variance functions

Song

Yang

2009

Asymptotically exact and conservative confidence bands are obtained for possibly heteroscedastic variance functions, using piecewise constant and piecewise linear spline estimation, respectively. The variance estimation is as efficient as an infeasible estimator when the conditional mean function is known, and the widths of the confidence bands are of optimal order. Simulation experiments provide strong evidence that corroborates the asymptotic theory while the computing is extremely fast. A slower bootstrap band is also proposed, with much higher accuracy. As illustrations, the bootstrap spline band has been applied to test for heteroscedasticity in fossil data and in motorcycle data.