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}
}
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… 

Figures and Tables from this paper

Jump-detection and curve estimation methods for discontinuous regression functions based on the piecewise B-spline function
ABSTRACT Jump-detection and curve estimation methods for the discontinuous regression function are proposed in this article. First, two estimators of the regression function based on B-splines are
Semiparametric jump-preserving estimation for single-index models
ABSTRACT Estimation of the single-index model with a discontinuous unknown link function is considered in this paper. Existed refined minimum average variance estimation (rMAVE) method can estimate
Lévy Adaptive B-spline Regression via Overcomplete Systems
TLDR
Results of simulation studies and real data examples support that this model catches not only smooth areas but also jumps and sharp peaks of functions and the proposed model has the best performance in almost all examples.
On functional processes with multiple discontinuities
We consider the problem of estimating multiple change points for a functional data process. There are numerous examples in science and finance in which the process of interest may be subject to some
Change-point regression with a smooth additive disturbance
  • F. Pein
  • Mathematics, Computer Science
  • 2021
TLDR
PCpluS, a combination of the fused Lasso and kernel smoothing, is proposed, a nonparametric regression model with signals given by the sum of a piecewise constant function and a smooth function when detecting change-points that argues that in this setting minimize the L1-loss is superior to minimizing the L2-loss.
Detecting multiple generalized change-points by isolating single ones
TLDR
This work introduces a new approach, called Isolate-Detect (ID), for the consistent estimation of the number and location of multiple generalized change-points in noisy data sequences, based on an isolation technique, which prevents the consideration of intervals that contain more than one change-point.
Narrowest‐over‐threshold detection of multiple change points and change‐point‐like features
TLDR
A new, generic and flexible methodology for non‐parametric function estimation, in which the number and locations of any features that may be present in the function and then estimate the function parametrically between each pair of neighbouring detected features is proposed.
Bayesian Selection for the $\ell _2$ -Potts Model Regularization Parameter: 1-D Piecewise Constant Signal Denoising
TLDR
This contribution proposes an operational strategy that combines hierarchical Bayesian and Potts model formulations, with the double aim of automatically tuning the regularization parameter and maintaining computational efficiency.
Measuring timeliness of annual reports filing by jump additive models
Foreign public issuers (FPIs) are required by the Securities and Exchanges Commission (SEC) to file Form 20-F as comprehensive annual reports. In an effort to increase the usefulness of 20-Fs, the
...
...

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
TLDR
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
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
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
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
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
TLDR
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
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
TLDR
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.
...
...