# Jump information criterion for statistical inference in estimating discontinuous curves

@article{Xia2012JumpIC,
title={Jump information criterion for statistical inference in estimating discontinuous curves},
author={Zhiming Xia and Peihua Qiu},
journal={Biometrika},
year={2012},
volume={102},
pages={397-408}
}
• Published 1 June 2015
• Mathematics, Computer Science
• Biometrika
Nonparametric regression analysis when the regression function is discontinuous has many applications. Existing methods for estimating a discontinuous regression curve usually assume that the number of jumps in the regression curve is known beforehand, which is unrealistic in some situations. Although there has been research on estimation of a discontinuous regression curve when the number of jumps is unknown, the problem remains mostly open because such research often requires assumptions on…

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## References

SHOWING 1-10 OF 36 REFERENCES
Spline Estimation of Discontinuous Regression Functions
Abstract This article deals with regression function estimation when the regression function is smooth at all but a finite number of points. An important question is: How can one produce
Jump Detection in a Regression Curve and Its Derivative
• Mathematics
Technometrics
• 2009
An alternative jump detection procedure is proposed, based on estimation of the (one-sided) first-order derivatives of the true regression curve, which works well in applications and is extended for detecting roofs/valleys of the regression curve.
Change point estimation by local linear smoothing
• Mathematics
• 2002
We consider the problem of estimating jump points in smooth curves. Observations (Xi, Yi) i = 1 ..... n from a random design regression function are given. We focus essentially on the basic situation
A local polynomial jump-detection algorithm in nonparametric regression
• Mathematics
• 1998
We suggest a one-dimensional jump-detection algorithm based on local polynomial fitting for jumps in regression functions (zero-order jumps) or jumps in derivatives (first-order or higherorder
Jump-Preserving Regression and Smoothing using Local Linear Fitting: A Compromise
• Mathematics
• 2007
This paper deals with nonparametric estimation of a regression curve, where the estimation method should preserve possible jumps in the curve. At each point x at which one wants to estimate the
Kernel-Type Estimators of Jump Points and Values of a Regression Function
• Mathematics
• 1993
In the fixed-design nonparametric regression model, kernel-type estimators of the locations of jump points and the corresponding sizes of jump values of the regression function are proposed. These
Bandwidth Selection for Changepoint Estimation in Nonparametric Regression
• Mathematics
Technometrics
• 2004
A bootstrap procedure for selecting the bandwidth parameters in a nonparametric two-step estimation method results in a fully data-driven procedure for estimating a finite (but possibly unknown) number of changepoints in a regression function.
A jump-detecting procedure based on spline estimation
• Mathematics
• 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
CHANGE-POINTS IN NONPARAMETRIC REGRESSION ANALYSIS'
an otherwise smooth regression model are proposed. The assumptions needed are much weaker than those made in parametric models. The proposed estimators apply as well to the detection of
Multiscale change point inference
• Mathematics, Computer Science
• 2013
A new estimator, the simultaneous multiscale change point estimator SMUCE, is introduced, which achieves the optimal detection rate of vanishing signals as n→∞, even for an unbounded number of change points.