Estimating the complexity index of functional data: Some asymptotics

E. G. Bongiorno; A. Goia; P. Vieu

doi:10.1016/j.spl.2020.108731

Estimating the complexity index of functional data: Some asymptotics

E. G. Bongiorno, A. Goia, P. Vieu

Department of Economics and Business Studies

Research output: Contribution to journal › Article › peer-review

Abstract

Consider a random curve valued in a general semi-metric space whose small-ball probability factorizes isolating the spatial and the volumetric term. Assume that the latter is specified and interprets its parameters as complexity indexes. An index estimate is constructed by comparing nonparametric versus parametric estimates of the volumetric factor, and various asymptotics (including weak convergence and asymptotic normality) are stated by means of U-statistics tools. As a by-product, new asymptotic results are stated for surrogate density estimation.

Original language	English
Article number	108731
Journal	Statistics and Probability Letters
Volume	161
DOIs	https://doi.org/10.1016/j.spl.2020.108731
Publication status	Published - Jun 2020

Keywords

Complexity index
Functional sample
Small ball probability
U-statistics

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10.1016/j.spl.2020.108731

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abstract = "Consider a random curve valued in a general semi-metric space whose small-ball probability factorizes isolating the spatial and the volumetric term. Assume that the latter is specified and interprets its parameters as complexity indexes. An index estimate is constructed by comparing nonparametric versus parametric estimates of the volumetric factor, and various asymptotics (including weak convergence and asymptotic normality) are stated by means of U-statistics tools. As a by-product, new asymptotic results are stated for surrogate density estimation.",

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Estimating the complexity index of functional data: Some asymptotics

Abstract

Keywords

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