Electronic Journal of Statistics

Simultaneous confidence bands for derivatives of dependent functional data

Guanqun Cao

Full-text: Open access

Abstract

In this work, consistent estimators and simultaneous confidence bands for the derivatives of mean functions are proposed when curves are repeatedly recorded for each subject. The within-curve correlation of trajectories has been considered while the proposed novel confidence bands still enjoys semiparametric efficiency. The proposed methods lead to a straightforward extension of the two-sample case in which we compare the derivatives of mean functions from two populations. We demonstrate in simulations that the proposed confidence bands are superior to existing approaches which ignore the within-curve dependence. The proposed methods are applied to investigate the derivatives of mortality rates from period lifetables that are repeatedly collected over many years for various countries.

Article information

Source
Electron. J. Statist., Volume 8, Number 2 (2014), 2639-2663.

Dates
First available in Project Euclid: 22 December 2014

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1419258189

Digital Object Identifier
doi:10.1214/14-EJS967

Mathematical Reviews number (MathSciNet)
MR3292952

Zentralblatt MATH identifier
1309.62074

Subjects
Primary: 62G08: Nonparametric regression 62G10: Hypothesis testing 62G15: Tolerance and confidence regions 62G20: Asymptotic properties

Keywords
B-spline confidence band derivatives functional data semiparametric efficiency repeated measures

Citation

Cao, Guanqun. Simultaneous confidence bands for derivatives of dependent functional data. Electron. J. Statist. 8 (2014), no. 2, 2639--2663. doi:10.1214/14-EJS967. https://projecteuclid.org/euclid.ejs/1419258189


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