## Bernoulli

• Bernoulli
• Volume 21, Number 2 (2015), 909-929.

### Two sample inference for the second-order property of temporally dependent functional data

#### Abstract

Motivated by the need to statistically quantify the difference between two spatio-temporal datasets that arise in climate downscaling studies, we propose new tests to detect the differences of the covariance operators and their associated characteristics of two functional time series. Our two sample tests are constructed on the basis of functional principal component analysis and self-normalization, the latter of which is a new studentization technique recently developed for the inference of a univariate time series. Compared to the existing tests, our SN-based tests allow for weak dependence within each sample and it is robust to the dependence between the two samples in the case of equal sample sizes. Asymptotic properties of the SN-based test statistics are derived under both the null and local alternatives. Through extensive simulations, our SN-based tests are shown to outperform existing alternatives in size and their powers are found to be respectable. The tests are then applied to the gridded climate model outputs and interpolated observations to detect the difference in their spatial dynamics.

#### Article information

Source
Bernoulli, Volume 21, Number 2 (2015), 909-929.

Dates
First available in Project Euclid: 21 April 2015

https://projecteuclid.org/euclid.bj/1429624965

Digital Object Identifier
doi:10.3150/13-BEJ592

Mathematical Reviews number (MathSciNet)
MR3338651

Zentralblatt MATH identifier
06445962

#### Citation

Zhang, Xianyang; Shao, Xiaofeng. Two sample inference for the second-order property of temporally dependent functional data. Bernoulli 21 (2015), no. 2, 909--929. doi:10.3150/13-BEJ592. https://projecteuclid.org/euclid.bj/1429624965

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#### Supplemental materials

• Supplementary material: Supplement to “Two sample inference for the second-order property of temporally dependent functional data”. This supplement contains proofs of the results in Section 3.