Simultaneous confidence band for stationary covariance function of dense functional data

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Abstract

The inference via simultaneous confidence band is studied for stationary covariance function of dense functional data. A two-stage estimation procedure is proposed based on spline approximation, the first stage involving estimation of all the individual trajectories and the second stage involving estimation of the covariance function through smoothing the empirical covariance function. The proposed covariance estimator is smooth and as efficient as the oracle estimator when all individual trajectories are known. An asymptotic simultaneous confidence band (SCB) is developed for the true covariance function, and the coverage probabilities are shown to be asymptotically correct. Intensive simulation experiments are conducted to demonstrate the performance of the proposed estimator and SCB. The proposed method is also illustrated with a real data example.

AMS 2010 subject classifications

primary
62H20
secondary
time series 62G08

Keywords

Confidence band
Covariance function
Functional data
Stationary process

Cited by (0)

1

Co-first author.