Functional time series prediction via conditional mode estimation

Ferraty, Frédéric; Laksaci, Ali; Vieu, Philippe

doi:10.1016/j.crma.2005.01.016

Cited by 28 publications

(15 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Furthermore, we suppose that ∈˚ , where˚ denotes the interior of . (D3) The joint density f * ij of Y i Y j exists and satisfies: sup u v f * ij u v − f * u f * v ≤ C < for some constant C not depending on i j (H) The bandwidth h satisfies: Ferraty et al (2005) and is needed to establish Lemma 5.4.…”

Section: Assumptions and Asymptotic Studymentioning

confidence: 99%

“…In a general ergodic framework, a process prediction via the conditional mode estimation was described by Ould-Saïd (1997) and its strong consistency was established. Recently, Ferraty et al (2005) established under -mixing condition, the almost complete convergence of the conditional mode of a scalar response given a functional random variable.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Strong Consistency Rate for the Kernel Mode Estimator Under Strong Mixing Hypothesis and Left Truncation

Ould-Saı̈d

Tatachak²

2009

Communications in Statistics - Theory and Methods

View full text Add to dashboard Cite

show abstract

Section: Assumptions and Asymptotic Studymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Strong Consistency Rate for the Kernel Mode Estimator Under Strong Mixing Hypothesis and Left Truncation

Ould-Saı̈d

Tatachak²

2009

Communications in Statistics - Theory and Methods

View full text Add to dashboard Cite

show abstract

“…(5) REML-based single-index signal regression with locally adaptive penalty (Wood, 2011); (6) nonparametric regression with NW estimator for estimating conditional mean (Ferraty and Vieu, 2006); (10) functional nonparametric regression with NW estimator for estimating conditional median (Laksaci et al, 2011); (11) functional nonparametric regression with NW estimator for estimating conditional mode (Ferraty et al, 2005); (12) functional nonparametric regression with k nearest neighbor estimator (Burba et al, 2009); (13) functional nonparametric regression with most-predictive design points (Ferraty et al, 2010a); (14) functional partial linear model.…”

Section: Spectrometric Data Analysismentioning

confidence: 99%

Bayesian bandwidth estimation and semi-metric selection for a functional partial linear model with unknown error density

Shang

2020

Journal of Applied Statistics

View full text Add to dashboard Cite

This study examines the optimal selections of bandwidth and semi-metric for a functional partial linear model. Our proposed method begins by estimating the unknown error density using a kernel density estimator of residuals, where the regression function, consisting of parametric and nonparametric components, can be estimated by functional principal component and functional Nadayara-Watson estimators. The estimation accuracy of the regression function and error density crucially depends on the optimal estimations of bandwidth and semi-metric. A Bayesian method is utilized to simultaneously estimate the bandwidths in the regression function and kernel error density by minimizing the Kullback-Leibler divergence. For estimating the regression function and error density, a series of simulation studies demonstrate that the functional partial linear model gives improved estimation and forecast accuracies compared with the functional principal component regression and functional nonparametric regression. Using a spectroscopy dataset, the functional partial linear model yields better forecast accuracy than some commonly used functional regression models. As a by-product of the Bayesian method, a pointwise prediction interval can be obtained, and marginal likelihood can be used to select the optimal semi-metric.

show abstract

“…The mode of the non‐parametrically estimated conditional distribution serves as an estimate of the conditional mode of y , whose convergence rate is derived by Ferraty et al. ().…”

Section: Generalisations and Extensionsmentioning

confidence: 99%

Methods for Scalar‐on‐Function Regression

Reiss

Goldsmith

Shang

et al. 2016

Int Statistical Rev

146

109

View full text Add to dashboard Cite

Recent years have seen an explosion of activity in the field of functional data analysis (FDA), in which curves, spectra, images, etc. are considered as basic functional data units. A central problem in FDA is how to fit regression models with scalar responses and functional data points as predictors. We review some of the main approaches to this problem, categorizing the basic model types as linear, nonlinear and nonparametric. We discuss publicly available software packages, and illustrate some of the procedures by application to a functional magnetic resonance imaging dataset.

show abstract

Functional time series prediction via conditional mode estimation

Cited by 28 publications

References 7 publications

Strong Consistency Rate for the Kernel Mode Estimator Under Strong Mixing Hypothesis and Left Truncation

Strong Consistency Rate for the Kernel Mode Estimator Under Strong Mixing Hypothesis and Left Truncation

Bayesian bandwidth estimation and semi-metric selection for a functional partial linear model with unknown error density

Methods for Scalar‐on‐Function Regression

Contact Info

Product

Resources

About