Simultaneous confidence bands for nonparametric regression with functional data

By David Degras. 2009

127 citations recorded by the source corpus.

We consider nonparametric regression in the context of functional data, that is, when a random sample of functions is observed on a fine grid. We obtain a functional asymptotic normality result allowing to build simultaneous confidence bands (SCB) for various estimation and inference tasks. Two applications to a SCB procedure for the regression function and to a goodness-of-fit test for curvilinear regression models are proposed. The first one has improved accuracy upon the other available methods while the second can detect local departures from a parametric shape, as opposed to the usual goodness-of-fit tests which only track global departures. A numerical study of the SCB procedures and an illustration with a speech data set are provided.

Subfields: Artificial Intelligence, Control and Systems Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/9d15ec088edeed0e9d7cda3813e4d9225a22a353

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Citations in the corpus

Functional Data Analysis (2016, background): “Another inference problem that has been explored is the construction of simultaneous conﬁdence bands for dense (Degras 2008, 2011; Wang & Yang 2009; Cao, Yang & Todem 2012) and sparse (Ma, Yang & Carroll 2012) functional data.”
Functional data analysis in the Banach space of continuous functions (2017, methodology): “The available work includes Degras [18], who dealt with confidence bands for nonparametric regression with functional data; Cao et al. [16], who studied simultaneous confidence bands for the mean of dense functional data based on polynomial spline estimators; Cao [15], who developed simultaneous con”
Functional Regression (2014, unknown): “Li & Hsing (2010) and Degras (2011) dealt with densely sampled functions and used local linear kernel approaches, and Bunea et al. (2011) used orthonormal basis functions.”
Horvitz--Thompson estimators for functional data: asymptotic confidence bands and optimal allocation for stratified sampling (2009, methodology): “We have proposed a simple rule to get confidence bands that could certainly be improved, in terms of empirical coverage, by computing more realistic scaling factors with bootstrap procedures (Faraway, 1997) or Gaussian process simulations (Degras, 2010).”