Abstract
SummaryWe propose a new, generic and flexible methodology for non-parametric function estimation, in which we first estimate 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. Examples of features handled by our methodology include change points in the piecewise constant signal model, kinks in the piecewise linear signal model and other similar irregularities, which we also refer to as generalized change points. Our methodology works with only minor modifications across a range of generalized change point scenarios, and we achieve such a high degree of generality by proposing and using a new multiple generalized change point detection device, termed narrowest-over-threshold (NOT) detection. The key ingredient of the NOT method is its focus on the smallest local sections of the data on which the existence of a feature is suspected. For selected scenarios, we show the consistency and near optimality of the NOT algorithm in detecting the number and locations of generalized change points. The NOT estimators are easy to implement and rapid to compute. Importantly, the NOT approach is easy to extend by the user to tailor to their own needs. Our methodology is implemented in the R package not.
Highlights
This paper considers the canonical univariate statistical modelYt = ft + "t, t = 1, : : :, T, .1/where the deterministic and unknown signal ft is believed to display some regularity across the index t, and the stochastic noise "t is exactly or approximately centred at zero
For the development of both theory and computation, in selected scenarios, we introduce the tailor-made contrast function that is derived from the generalized likelihood ratio (GLR)
B&P allows for change point detection in piecewise linear and piecewise quadratic signals; we study the performance of the trend filtering methodology of Kim et al (2009) termed TF
Summary
This paper considers the canonical univariate statistical model. Despite the simplicity of model (1), inferring information about ft remains a task of fundamental importance in modern applied statistics and data science. If ft is modelled as piecewise constant and it is of interest to detect its change points, several techniques are available, and we mention only a selection. For Gaussian noise "t, both nonpenalized and penalized least squares approaches were considered by Yao and Au (1989). Frick et al (2014) provided confidence intervals for the location of the estimated change points. Often this penaltytype approach requires a computational cost of at least O.T 2/.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Journal of the Royal Statistical Society Series B: Statistical Methodology
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
