Index Models for Sparsely Sampled Functional Data

Radchenko, Peter; Qiao, Xinghao; James, Gareth

doi:10.1080/01621459.2014.931859

Cited by 15 publications

(7 citation statements)

References 29 publications

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“…In some fields of functional data analysis, noisy random functions have already been studied intensively; a body of literature on this topic encompassing functional linear regression, functional principal components, continuous additive models, etc. can be found in Yao et al (2005), Crambes et al (2009), Paul and Peng (2009), Jiang and Wang (2010), Li and Hsing (2010), Wu et al (2010), Müller et al (2013), Radchenko et al (2015), Hsing and Eubank (2015) and Zhang and Wang (2016), among others. In those works, noisy functional data are typically either (i) pre-smoothed in the first step, and then statistical analysis is performed for the smoothed approximants of the data curves; or (ii) the statistical procedure in question is revisited, and suitably applied directly to the available discrete noisy observations.…”

Section: Introductionmentioning

confidence: 94%

Data depth for measurable noisy random functions

Nagy¹,

Ferraty

2019

Journal of Multivariate Analysis

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In the literature on data depth applicable to random functions it is usually assumed that the trajectories of all the random curves are continuous, known at each point of the domain, and observed exactly. These assumptions turn out to be unrealistic in practice, as the functions are often observed only at a finite grid of time points, and in the presence of measurement errors. In this work, we provide the necessary theoretical background enabling the extension of the statistical methodology based on data depth to measurable (not necessarily continuous) random functions observed within the latter framework. It is shown that even if the random functions are discontinuous, observed discretely, and contaminated with additive noise, many common depth functionals maintain the fine consistency properties valid in the ideal case of completely observed noiseless functions. For the integrated depth for functions, we provide uniform rates of convergence over the space of integrable functions.

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Section: Introductionmentioning

confidence: 94%

Data depth for measurable noisy random functions

Nagy¹,

Ferraty

2019

Journal of Multivariate Analysis

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“…Then we obtain the estimate r S k puq " p b pkq 0 . We also develop a basis expansion approach (Radchenko et al, 2015) to estimate C k and S k , where details can be found in Section C of the Supplementary Material.…”

Section: Partially Observed Functional Predictormentioning

confidence: 99%

Functional Linear Regression: Dependence and Error Contamination

Chen

Guo

Qiao

2020

Journal of Business & Economic Statistics

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Functional linear regression is an important topic in functional data analysis. It is commonly assumed that samples of the functional predictor are independent realizations of an underlying stochastic process, and are observed over a grid of points contaminated by i.i.d. measurement errors. In practice, however, the dynamical dependence across different curves may exist and the parametric assumption on the error covariance structure could be unrealistic. In this paper, we consider functional linear regression with serially dependent observations of the functional predictor, when the contamination of the predictor by the white noise is genuinely functional with fully nonparametric covariance structure. Inspired by the fact that the autocovariance function of observed functional predictors automatically filters out the impact from the unobservable noise term, we propose a novel autocovariance-based generalized method-of-moments estimate of the slope function. We also develop a nonparametric smoothing approach to handle the scenario of partially observed functional predictors. The asymptotic properties of the resulting estimators under different scenarios are established. Finally, we demonstrate that our proposed method significantly outperforms possible competing methods through an extensive set of simulations and an analysis of a public financial dataset.

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“…Other nonparametric functional regression approaches are Preda (2007); Lian (2007,2011). Semiparametric approaches are relatively less-studied and scattered in the literature including Ait-Saidi et al (2008); Müller and Yao (2008); Chen et al (2011); McLean et al (2014); Zhu et al (2014); Radchenko et al (2015), among some others.…”

Section: Introductionmentioning

confidence: 99%

Partially Linear Additive Functional Regression

Liu¹,

Lü²,

Lian³

et al. 2023

STAT SINICA

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We consider a novel partially linear additive functional regression model in which both a functional predictor and some scalar predictors appear. The functional part has a semiparametric continuously additive form while the scalar predictors enter in the linear part. The functional part has the optimal convergence rate and asymptotic normality of the non-functional part is also shown. Some simulations and an empirical analysis of a COVID-19 data set are used to demonstrate the performances of the proposed estimator.

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Index Models for Sparsely Sampled Functional Data

Cited by 15 publications

References 29 publications

Data depth for measurable noisy random functions

Data depth for measurable noisy random functions

Functional Linear Regression: Dependence and Error Contamination

Partially Linear Additive Functional Regression

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