Nonparametric modelling for functional data: selected survey and tracks for future

Ling, Nengxiang; Vieu, Philippe

doi:10.1080/02331888.2018.1487120

Cited by 98 publications

(39 citation statements)

References 139 publications

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“…Focusing for simplicity on the case with functional regressors and scalar response, the main effect of having explanatory variables in a possibly infinite‐dimensional space with a metric d is that the nonparametric estimation has to rely on the metric d instead of the simple Euclidian distance (Ling & Vieu, ) and the nonparametric M ‐estimator (10) at some point x becomes now

n^{- 1} \sum_{i = 1}^{n} ψ ((), y_{i} - a) K ((), \frac{d (x_{i}, x)}{h}) = 0 .

…”

Section: Other Nonparametric Regression Modelsmentioning

confidence: 99%

Robust nonparametric regression: A review

Čı́žek

Sadikoglu

2019

WIREs Computational Stats

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Nonparametric regression methods provide an alternative approach to parametric estimation that requires only weak identification assumptions and thus minimizes the risk of model misspecification. In this article, we survey some nonparametric regression techniques, with an emphasis on kernel-based estimation, that are additionally robust to atypical and outlying observations. While the main focus lies on robust regression estimation, robust bandwidth selection and conditional scale estimation are discussed as well. Robust estimation in popular nonparametric models such as additive and varying-coefficient models is summarized too. The performance of the main methods is demonstrated on a real dataset. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Robust Methods Statistical and Graphical Methods of Data Analysis > Nonparametric Methods K E Y W O R D S nonparametric regression, outliers, robust estimation 1 | INTRODUCTIONNonparametric regression models have received substantial attention in the theoretical and applied statistics literature over the last few decades. The underlying reason for their growing popularity and importance is that they do not rely on any particular form of the regression function characterizing the relationship between the dependent and explanatory variables and that they are thus robust to model misspecification. On the other hand, many classical nonparametric estimators are not robust in the sense that they are sensitive to atypical and outlying observations in the data. To address this, many authors have explored robust nonparametric regression estimation. As many nonparametric estimators of the regression function are local versions of the estimators of the location-scale model or the linear regression model, many initially proposed robust nonparametric regression estimators were inspired by the developments and construction of robust estimators in those two simple models, which we briefly recall in Section 1.1. Later, we introduce the main concepts of nonparametric regression in Section 1.2 and discuss the robust nonparametric methods from Section 2 on. | Robust estimation of the location and regression modelsConsider the simple univariate location-scale model Y = μ + σε, where Y is a continuously distributed univariate random variable, μ and σ are the location and scale parameters, respectively, and ϵ is an error term. For a random sample

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n^{- 1} \sum_{i = 1}^{n} ψ ((), y_{i} - a) K ((), \frac{d (x_{i}, x)}{h}) = 0 .

…”

Section: Other Nonparametric Regression Modelsmentioning

confidence: 99%

Robust nonparametric regression: A review

Čı́žek

Sadikoglu

2019

WIREs Computational Stats

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“…FDA was 20 ago a very confidential area of researches and its popularization started really with Ramsay and Silverman's books (see Ramsay & Silverman, 1996, 2002, 2005). Twenty years later, many among standard multivariate statistical procedures have been adapted to functional data and there is now a wide literature on FDA as attested by the books (Aneiros, Bongiorno, Cao, & Vieu, 2017; Bongiorno, Goia, Salinelli, & Vieu, 2014; Bosq, 2000; Bosq & Blanke, 2007; Ferraty & Vieu, 2006; Horváth & Kokoszka, 2012; Hsing & Eubank, 2015; Shi & Choi, 2011; Zhang, 2013a), and by various bibliographical discussions such as Aneiros, Cao, and Vieu (2019), Aneiros, Cao, Fraiman, Genest, and Vieu (2019), Cuevas (2014), Geenens (2011), Goia and Vieu (2016), Horváth and Rice (2015), Jacques and Preda (2014), Ling and Vieu (2018), Müller and Hall (2016), Nagy (2017), Shang (2014a), and Vieu (2018).…”

Section: Introductionmentioning

confidence: 99%

On semiparametric regression in functional data analysis

Ling

Vieu

2020

WIREs Computational Stats

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The aim of this paper is to provide a selected advanced review on semiparametric regression which is an emergent promising field of researches in functional data analysis. As a deliberate strategy, we decided to focus our discussion on the single functional index regression (SFIR) model in order to fix the ideas about the stakes linked with infinite dimensional problems and about the methodological challenges that one has to solve when building statistical procedure: one of the most challenging issue being the question of dimensionality effects reduction. This will be the first (and the main) part of this discussion and a complete survey of the literature on SFIR model will be presented. In a second attempt, other semiparametric models (and more generally, other dimension reduction models) will be shortly discussed with the double goal of presenting the state of art and of defining challenging tracks for the future. At the end, we will discuss how additive modeling is an appealing idea for more complicated models involving multifunctional predictors and some tracks for the future will be pointed in this setting. This article is categorized under: Statistical Models > Semiparametric Models Data: Types and Structure > Time Series, Stochastic Processes, and Functional Data Statistical Learning and Exploratory Methods of the Data Sciences > Modeling Methods

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“…For more references on the state of the art on FDA, the reader can refer to the Cuevas (2014)'s survey document which brings together a wide range of statistical methods adapted to the modeling of functional data. While Ling and Vieu (2018) take up some recent advances with nonparametric methods and discuss important perspectives for future advances. In this paper, we build a new nonparametric estimator of the functional regression model by combining the local linear (LC) procedure with the kNN smoothing approach.…”

Section: Introductionmentioning

confidence: 99%

k‐Nearest neighbors local linear regression for functional and missing data at random

Rachdi

Laksaci

Kaid

et al. 2020

Statistica Neerlandica

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We combine the k‐Nearest Neighbors (kNN) method to the local linear estimation (LLE) approach to construct a new estimator (LLE‐kNN) of the regression operator when the regressor is of functional type and the response variable is a scalar but observed with some missing at random (MAR) observations. The resulting estimator inherits many of the advantages of both approaches (kNN and LLE methods). This is confirmed by the established asymptotic results, in terms of the pointwise and uniform almost complete consistencies, and the precise convergence rates. In addition, a numerical study (i) on simulated data, then (ii) on a real dataset concerning the sugar quality using fluorescence data, were conducted. This practical study clearly shows the feasibility and the superiority of the LLE‐kNN estimator compared to competitive estimators.

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Nonparametric modelling for functional data: selected survey and tracks for future

Cited by 98 publications

References 139 publications

Robust nonparametric regression: A review

Robust nonparametric regression: A review

On semiparametric regression in functional data analysis

k‐Nearest neighbors local linear regression for functional and missing data at random

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