Nonparametric Functional Methods: New Tools for Chemometric Analysis

Ferraty, Frédéric; Goia, Aldo; Vieu, Philippe

doi:10.1007/978-3-540-32691-5_13

Cited by 61 publications

(105 citation statements)

References 15 publications

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“…When prediction is the primary goal, kernel nonparametric regression techniques combined with functional PCA are widely applied [2,[23][24][25]. We used a nonparametric functional PCA method that is implemented in the Matlab package PACE (Principal Analysis by Conditional Expectation; http://www.stat.ucdavis.edu/PACE/) to estimate eigenfunctions, where the number of eigenfunctions is chosen by one-curve-leave-out cross-validation procedures [48].…”

Section: Prediction Comparisonmentioning

confidence: 99%

Functional envelope for model-free sufficient dimension reduction

Zhang

Wang

2018

Journal of Multivariate Analysis

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Section: Prediction Comparisonmentioning

confidence: 99%

Functional envelope for model-free sufficient dimension reduction

Zhang

Wang

2018

Journal of Multivariate Analysis

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“…nal linear  odel 0.1 is known as functional nonparametric regression model [6]. A review of the main results and spectroscopy applications of this model appears in [20].…”

Section: Functional Linear Regressionmentioning

confidence: 99%

“…In both cases the computational algorithm has the steps  Computation and selection by cross-validation of a set of m components [21] and its application to classify spectrometric data revised in [20]. Functional logit regression and functional linear discriminant analysis that have been used in different applications with chemometrics data are summarized hereafter.…”

Section: Amentioning

confidence: 99%

“…Different estimates of these models based on PCA and PLS have been considered for the successful implementation of these techniques [3,[16][17][18][19]. The lector interested in a review of functional nonparametric methods for solving the problems of regression and classification of curves, and as well as known applications in spectroscopy , must be referred to [20].…”

Section: Introductionmentioning

confidence: 99%

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Functional Analysis of Chemometric Data

M.¹,

Escabias²,

J.³

et al. 2013

OJS

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The objective of this paper is to present a review of different calibration and classification methods for functional data in the context of chemometric applications. In chemometric, it is usual to measure certain parameters in terms of a set of spectrometric curves that are observed in a finite set of points (functional data). Although the predictor variable is clearly functional, this problem is usually solved by using multivariate calibration techniques that consider it as a finite set of variables associated with the observed points (wavelengths or times). But these explicative variables are highly correlated and it is therefore more informative to reconstruct first the true functional form of the predictor curves. Although it has been published in several articles related to the implementation of functional data analysis techniques in chemometric, their power to solve real problems is not yet well known. Because of this the extension of multivariate calibration techniques (linear regression, principal component regression and partial least squares) and classification methods (linear discriminant analysis and logistic regression) to the functional domain and some relevant chemometric applications are reviewed in this paper.

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“…Nonparametric or structure-free methods for curve estimation from functional data involve the concept of density, not least because they generally are based on estimators of Nadaraya-Watson type which require di-vision by an estimator of a small-ball probability. See, for example, Ferraty, Goïa and Vieu (2002a, 2002b, 2007a, 2007b, Ferraty and Vieu (2002, 2003, 2004, 2006a, 2006b and Niang (2002). There is of course a more general and very large methodology for functional data analysis, accessible via the monographs by Silverman (2002, 2005).…”

mentioning

confidence: 99%

Defining probability density for a distribution of random functions

Delaigle¹,

Hall²

2010

Ann. Statist.

109

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The notion of probability density for a random function is not as straightforward as in finite-dimensional cases. While a probability density function generally does not exist for functional data, we show that it is possible to develop the notion of density when functional data are considered in the space determined by the eigenfunctions of principal component analysis. This leads to a transparent and meaningful surrogate for density defined in terms of the average value of the logarithms of the densities of the distributions of principal components for a given dimension. This density approximation is estimable readily from data. It accurately represents, in a monotone way, key features of small-ball approximations to density. Our results on estimators of the densities of principal component scores are also of independent interest; they reveal interesting shape differences that have not previously been considered. The statistical implications of these results and properties are identified and discussed, and practical ramifications are illustrated in numerical work.Comment: Published in at http://dx.doi.org/10.1214/09-AOS741 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

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Nonparametric Functional Methods: New Tools for Chemometric Analysis

Cited by 61 publications

References 15 publications

Functional envelope for model-free sufficient dimension reduction

Functional envelope for model-free sufficient dimension reduction

Functional Analysis of Chemometric Data

Defining probability density for a distribution of random functions

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