Nonparametric models for functional data, with application in regression, time series prediction and curve discrimination

By Frédéric Ferraty, Philippe Vieu. 2004

185 citations recorded by the source corpus.

Subfields: Analytical Chemistry, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/2669f837c2ac2cd4ab7bb260ad451f8be5ecf74c

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In Analytical Chemistry

In Statistics and Probability

Citations in the corpus

Empirical likelihood confidence intervals for nonparametric functional data analysis (2009, methodology): “We note that the term µ0− r(x0) is same as the bias term in estimating r(x0) and thus |µ0 − r(x0)| = O(hα) = o((nφ(h))−1/2) by the results in Ferraty and Vieu (2004) and the assumption nh2αφ(h) → 0.”
Robust forecasting of mortality and fertility rates: A functional data approach (2007, methodology): “The nonparametric functional data analysis discussed by Ferraty and Vieu (2004) differs from our approach in that they look at the problem with a scalar response variable and a functional covariate.”
Defining probability density for a distribution of random functions (2010, background): “For example, it underpins discussion of the mode of the distribution of a random function, addressed in particular by Gasser, Hall and Presnell (1998), Hall and Heckman (2002) and Dabo-Niang, Ferraty and Vieu (2004a, 2004b, 2006).”
Fourier analysis of stationary time series in function space (2013, background): “Problems considered include that of the estimation of the second-order structure [e.g., Mas (2000), Bosq (2002), Dehling and Sharipov (2005)] and that of prediction [e.g., Antoniadis and Sapatinas (2003), Ferraty and Vieu (2004), Antoniadis, Paparoditis and Sapatinas (2006)].”
Functional Modelling and Classification of Longitudinal Data * (2005, background): “Such approaches are discussed in Ferraty & Vieu (2004) and Rice (2004) and open up promising avenues for future research in FDA.”
Assessing the finite dimensionality of functional data (2006, background): “See particularly Ferraty and Vieu (2003, 2004), who discussed the importance of semimetrics in this setting.”
Asymptotic Results of a Nonparametric Conditional Quantile Estimator for Functional Time Series (2008, background): “For instance, Ferraty and Vieu ( 2004 ) established the strong consistency of kernel estimators of the regression function when the explanatory variable is functional and the response is scalar.”
Single and multiple index functional regression models with nonparametric link (2011, methodology): “Fully nonparametric methods have been studied recently in functional-data regression and related problems (see, for example, [15], [13] and [21]).”
Prediction in functional linear regression (2006, methodology): “Other recent work on regression for functional data includes that of Ferré and Yao [18], who introduced a functional version of sliced inverse regression; Preda and Saporta [26], who discussed linear regression on clusters of functional data; Escabias, Aguilera and Valderrama [14] and Ratcliffe, He”
Nonparametric modelling for functional data: selected survey and tracks for future (2018, background): “First studies are based on mixing conditions on the sample: complete convergence results of type (4) were firstly presented for basic kernel estimate (3) in [60] and extended in [4,61,62], while uniform rates of type (5) were presented in [63] (see [64]) and asymptotic normality was stated in [65] a”
Convergence of functional k-nearest neighbor regression estimate with functional responses (2011, background): “Its importance has been demonstrated in [10, 11, 8] for functional kernel regression.”