Dependent Functional Data

Kokoszka, Piotr

doi:10.5402/2012/958254

Cited by 20 publications

(18 citation statements)

References 64 publications

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“…, n, defining the system of stochastic differential or pseudodifferential equations (9). Covariance operator estimation has been addressed in [8], [38] and [43].…”

Section: Remarkmentioning

confidence: 99%

Functional analysis of variance for Hilbert-valued multivariate fixed effect models

Ruiz-Medina

2015

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This paper presents new results on Functional Analysis of Variance for fixed effect models with correlated Hilbert-valued Gaussian error components. The geometry of the Reproducing Kernel Hilbert Space (RKHS) of the error term is considered in the computation of the total sum of squares, the residual sum of squares, and the sum of squares due to the regression. Under suitable linear transformation of the correlated functional data, the distributional characteristics of these statistics, their moment generating and characteristic functions, are derived. Fixed effect linear hypothesis testing is finally formulated in the Hilbert-valued multivariate Gaussian context considered.

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“…, n, defining the system of stochastic differential or pseudodifferential equations (9). Covariance operator estimation has been addressed in [8], [38] and [43].…”

Section: Remarkmentioning

confidence: 99%

Functional analysis of variance for Hilbert-valued multivariate fixed effect models

Ruiz-Medina

2015

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“…Many functional data sets, most notably in finance and environmental sciences, arise from long records of observations. This gives additional support to treat these data as a time series of evolving shape curves, which we will call a Functional Time Series (Bosq (1991), Bosq (2000), Kokoszka (2012)). Following Bosq (1991), the main idea behind functional time series modeling is that in many situations the time record can be split into natural intervals, and instead of modeling periodicity, we treat the curve in each interval as a whole observational unit.…”

Section: Introductionmentioning

confidence: 99%

Non parametric learning approach to estimate conditional quantiles in the dependent functional data case

Henchiri

2016

Communications in Statistics - Theory and Methods

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In this paper, we focus on conditional quantile estimation when the covariates take their values in a bounded subspace of the functional space L 2 (T ), of square integrable random functions defined on some compact set T . We use a nonparametric learning approach based on Support Vector Machines technique. The main goal is to establish a weak consistency of the Support Vector Machines estimator of conditional quantile under exponentially strongly mixing functional input sequences. Our main result (the estimator satisfies an oracle inequality) extends a previous result for independent and identically distributed sample. We apply this estimator in practice through a real dataset study.

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“…Cf., e.g.,Kokoszka (2012),Aue & Horváth (2013) and the invited discussion paper by.2 Cf., also andBerkes et al (2015).…”

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confidence: 99%

A Darling–Erdős-type CUSUM-procedure for functional data

Torgovitski

2014

Metrika

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This article considers testing for mean-level shifts in functional data. The class of the famous Darling-Erdős-type cumulative sums (CUSUM) procedures is extended to functional time series under short range dependence conditions which are satisfied by functional analogues of many popular time series models including the linear functional AR and the non-linear functional ARCH. We follow a data driven, projection-based approach where the lower-dimensional subspace is determined by (long run) functional principal components which are eigenfunctions of the long run covariance operator. This second-order structure is generally unknown and estimation is crucial -it plays an even more important role than in the classical univariate setup because it generates the finitedimensional subspaces. We discuss suitable estimates and demonstrate empirically that altogether this change-point procedure performs well under moderate temporal dependence.Moreover, Darling-Erdős-type change-point estimates based on (long run) functional principal components as well as the corresponding »fully-functional« counterparts are provided and the testing procedure is finally applied to publicly accessible electricity data from a German power company.

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Dependent Functional Data

Cited by 20 publications

References 64 publications

Functional analysis of variance for Hilbert-valued multivariate fixed effect models

Functional analysis of variance for Hilbert-valued multivariate fixed effect models

Non parametric learning approach to estimate conditional quantiles in the dependent functional data case

A Darling–Erdős-type CUSUM-procedure for functional data

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