PCA‐based discrimination of partially observed functional data, with an application to AneuRisk65 data set

Stefanucci, Marco; Sangalli, Laura M.; Brutti, Pierpaolo

doi:10.1111/stan.12137

Cited by 17 publications

(10 citation statements)

References 24 publications

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“…Several recent works have begun addressing the estimation of covariance functions for short functional segments observed at sparse and irregular grid points, called "functional snippets", (Descary and Panaretos (2019); ; Lin, Wang, and Zhong (2020); Zhang and Chen (2020)), or for fragmented functional data observed on small subintervals (Delaigle, Hall, Huang, and Kneip (2020)). For densely observed partial data, existing studies include the estimation of the unobserved part of curves (Kraus (2015); Delaigle and Hall (2016); Kneip and Liebl (2019)), prediction (Liebl (2013); Goldberg, Ritov, and Mandelbaum (2014)), classification (Delaigle and Hall (2013); Stefanucci, Sangalli, and Brutti (2018); Mojirsheibani and Shaw (2018); Kraus and Stefanucci (2018); Park and Simpson (2019)), functional regression (Gellar et al (2014)), and inferences (Gromenko, Kokoszka, and Sojka (2017); Kraus (2019)).…”

Section: Introductionmentioning

confidence: 99%

Robust Inference for Partially Observed Functional Response Data

Park¹,

Chen²,

Simpson³

2023

STAT SINICA

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Irregular functional data in which densely sampled curves are observed over different ranges pose a challenge for modeling and inference, and sensitivity to outlier curves is a concern in applications. Motivated by applications in quantitative ultrasound signal analysis, this paper investigates a class of robust M-estimators for partially observed functional data including functional location and quantile estimators. Consistency of the estimators is established under general conditions on the partial observation process. Under smoothness conditions on the class of M-estimators, asymptotic Gaussian process approximations are established and used for large sample inference. The large sample approximations justify a bootstrap approximation for robust inferences about the functional response process.The performance is demonstrated in simulations and in the analysis of irregular functional data from quantitative ultrasound analysis.

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Section: Introductionmentioning

confidence: 99%

Robust Inference for Partially Observed Functional Response Data

Park¹,

Chen²,

Simpson³

2023

STAT SINICA

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“…, X n is observed on a set O i ⊆ I, while no information about the curves is available on the missing sets M i = I \ O i . This type of partially observed functions was previously considered by, e.g., Bugni (2012), Delaigle and Hall (2013), Liebl (2013), Gellar et al (2014), Goldberg et al (2014), Kraus (2015), Delaigle and Hall (2016), Gromenko et al (2017), Dawson and Müller (2018), Mojirsheibani and Shaw (2018), Stefanucci et al (2018), Descary and Panaretos (2019), Kneip and Liebl (2020), Kraus (2019), Kraus and Stefanucci (2019) or Liebl and Rameseder (2019). In this paper we deal with function reconstruction (completion), that is, with the task to estimate, or rather predict the missing parts of curves from the observed parts.…”

Section: Introductionmentioning

confidence: 99%

Ridge reconstruction of partially observed functional data is asymptotically optimal

Kraus

Stefanucci

2020

Statistics & Probability Letters

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When functional data are observed on parts of the domain, it is of interest to recover the missing parts of curves. Kraus (2015) proposed a linear reconstruction method based on ridge regularization. Kneip and Liebl (2020) argue that an assumption under which Kraus (2015) established the consistency of the ridge method is too restrictive and propose a principal component reconstruction method that they prove to be asymptotically optimal. In this note we relax the restrictive assumption that the true best linear reconstruction operator is Hilbert-Schmidt and prove that the ridge method achieves asymptotic optimality under essentially no assumptions. The result is illustrated in a simulation study.

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“…In other words, for non-snippet functional data and for each (s, t) ∈ [a, b] 2 , one has Pr{(s, t) ∈ n i=1 [A i , B i ] 2 } > 0 for sufficiently large n, contrasting with (1) for functional snippets. Other related works by Gellar et al (2014); Goldberg et al (2014); Gromenko et al (2017); Stefanucci et al (2018) on partially observed functional data, although do not explicitly discuss the design, require condition (F) for their proposed methodologies and theory. All of them can be handled with a proper interpolation method, which is fundamentally different from the extrapolation methods needed for functional snippets.…”

Section: Introductionmentioning

confidence: 99%

Mean and Covariance Estimation for Functional Snippets

Lin,

Wang

2020

Preprint

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We consider estimation of mean and covariance functions of functional snippets, which are short segments of functions possibly observed irregularly on an individual specific subinterval that is much shorter than the entire study interval. Estimation of the covariance function for functional snippets is challenging since information for the far off-diagonal regions of the covariance structure is completely missing. We address this difficulty by decomposing the covariance function into a variance function component and a correlation function component. The variance function can be effectively estimated nonparametrically, while the correlation part is modeled parametrically, possibly with an increasing number of parameters, to handle the missing information in the far off-diagonal regions. Both theoretical analysis and numerical simulations suggest that this hybrid strategy is effective. In addition, we propose a new estimator for the variance of measurement errors and analyze its asymptotic properties. This estimator is required for the estimation of the variance function from noisy measurements.

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PCA‐based discrimination of partially observed functional data, with an application to AneuRisk65 data set

Cited by 17 publications

References 24 publications

Robust Inference for Partially Observed Functional Response Data

Robust Inference for Partially Observed Functional Response Data

Ridge reconstruction of partially observed functional data is asymptotically optimal

Mean and Covariance Estimation for Functional Snippets

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