 Data depth for measurable noisy random functionsStanislav Nagy and Frédéric Ferraty Journal of Multivariate Analysis, 2019, vol. 170, issue C, 95-114 Abstract: 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 on 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. Keywords: Asymptotics; Data depth; Functional data; Measurement error; Rate of convergence; Smoothing (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:170:y:2019:i:c:p:95-114 Ordering information: This journal article can be ordered from DOI: 10.1016/j.jmva.2018.11.003 Access Statistics for this article Journal of Multivariate Analysis is currently edited by de Leeuw, J. More articles in Journal of Multivariate Analysis from Elsevier |
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