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Mean and Covariance Estimation for Functional Snippets

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. Supplementary materials for this article are available online.

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Informasi Detail

Judul Seri

JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION; Vol.117 No.537 March 2022

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 348-360

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

CORRELATION FUNCTION
FUNCTIONAL DATA ANALYSIS
FUNCTIONAL PRINCIPAL COMPONENT ANALYSIS
VARIANCE FUNCTION
SPARSE FUNCTIONAL DATA

Info Detail Spesifik

https://doi.org/10.1080/01621459.2020.1777138

Pernyataan Tanggungjawab

Zhenhua Lin, Jane-Ling Wang

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