Approximation of estimators in the PCA of a stochastic process using B-splines

Aguilera, Ana M.; Gutiérrez, Ramón; Valderrama, Mariano J.

doi:10.1080/03610919608813336

Cited by 30 publications

(18 citation statements)

References 10 publications

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“…A solution by expanding sample-paths in terms of B-spline functions was proposed in Aguilera et al (1996). Ramsay and Silverman (2005) also propose the expression of observed functions as linear combinations of B-splines functions forming an approximate base of L 2 (I).…”

Section: Functional Principal Component Analysis (Fpca)mentioning

confidence: 99%

Analysing musical performance through functional data analysis: rhythmic structure in Schumann'sTräumerei

Almansa

Delicado

2009

Connection Science

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Functional Data Analysis is a relatively new branch of Statistics devoted to describing and modelling data that are complete functions. Many relevant aspects of musical performance and perception can be understood and quantified as dynamic processes evolving as functions of time. In this paper, we show that Functional Data Analysis is a statistical methodology well-suited for research into the field of quantitative musical performance analysis. To demonstrate this suitability, we consider tempo data for 28 performances of Schumann's Träumerei and analyse them by means of functional principal component analysis (one of the most powerful descriptive tools included in Functional Data Analysis). Specifically, we investigate the commonalities and differences between different performances regarding (expressive) timing, and we cluster similar performances together. We conclude that musical data considered as functional data reveals performance structures that otherwise might go unnoticed.

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Section: Functional Principal Component Analysis (Fpca)mentioning

confidence: 99%

Analysing musical performance through functional data analysis: rhythmic structure in Schumann'sTräumerei

Almansa

Delicado

2009

Connection Science

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“…On the one hand, least squares approximation on the space generated by the basis can be used if we consider that the observations are obtained with some error (Aguilera et al, 1995). On the other hand, interpolation can be used if we consider that the observations are obtained without error (Aguilera et al, 1996).…”

Section: Approximating the Parameter Function By Quasi-natural Cubic mentioning

confidence: 99%

“…The most used approximated solution for this estimation problem is to consider that functional observations belong to a space generated by a basis of functions and to make a multiple treatment based on this approach. Different bases have been used in the literature as trigonometric functions (Ramsay and Silverman (1997) and Aguilera et al (1995)), spline functions (Aguilera et al, 1996) or wavelets functions (Ocaña et al, 1998).…”

Section: Introductionmentioning

confidence: 99%

Modeling environmental data by functional principal component logistic regression

2004

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SUMMARYIn recent years, many studies have dealt with predicting a response variable based on the information provided by a functional variable. When the response variable is binary, different problems arise, such as multicollinearity and high dimensionality, which prejudice the estimation of the model and the interpretation of its parameters. In this article we address these problems by using functional logistic regression and principal component analysis. In order to obtain a unique solution for the maximum likelihood estimation of the parameter function, quasi-natural cubic spline interpolation of sample paths on their discrete time observations is proposed. We also introduce a new interpretation of the relationship between the response variable and the functional predictor where the change in the odds of success is evaluated from the estimated parameter function. An analysis of climatological data is finally presented to illustrate the practical performance of the proposed methodologies.

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“…In the application carried out below, the algorithm developed by the authors for the non-periodic case is used, where the functions are base B-splines (Aguilera et al, 1996a). The B-splines have compact support, that is, they are zero everywhere except over a finite interval.…”

Section: Estimation Of the Functional Techniquesmentioning

confidence: 99%

Explaining functional principal component analysis to actuarial science with an example on vehicle insurance

Segovia-González

Guerrero

Herranz

2009

Insurance: Mathematics and Economics

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Approximation of estimators in the PCA of a stochastic process using B-splines

Cited by 30 publications

References 10 publications

Analysing musical performance through functional data analysis: rhythmic structure in Schumann'sTräumerei

Analysing musical performance through functional data analysis: rhythmic structure in Schumann'sTräumerei

Modeling environmental data by functional principal component logistic regression

Explaining functional principal component analysis to actuarial science with an example on vehicle insurance

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