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Finite sample theory for high-dimensional functional/scalar time series with applications

Fang, Qin, Guo, Shaojun and Qiao, Xinghao ORCID: 0000-0002-6546-6595 (2022) Finite sample theory for high-dimensional functional/scalar time series with applications. Electronic Journal of Statistics, 16 (1). 527 - 591. ISSN 1935-7524

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Identification Number: 10.1214/21-EJS1960


Statistical analysis of high-dimensional functional times series arises in various applications. Under this scenario, in addition to the intrinsic infinite-dimensionality of functional data, the number of functional variables can grow with the number of serially dependent observations. In this paper, we focus on the theoretical analysis of relevant estimated cross-(auto)covariance terms between two multivariate functional time series or a mixture of multivariate functional and scalar time series beyond the Gaussianity assumption. We introduce a new perspective on dependence by proposing functional cross-spectral stability measure to characterize the effect of dependence on these estimated cross terms, which are essential in the estimates for additive functional linear regressions. With the proposed functional cross-spectral stability measure, we develop useful concentration inequalities for estimated cross-(auto)covariance matrix functions to accommodate more general sub-Gaussian functional linear processes and, furthermore, establish finite sample theory for relevant estimated terms under a commonly adopted functional principal component analysis framework. Using our derived non-asymptotic results, we investigate the convergence properties of the regularized estimates for two additive functional linear regression applications under sparsity assumptions including functional linear lagged regression and partially functional linear regression in the context of high-dimensional functional/scalar time series.

Item Type: Article
Official URL:
Additional Information: © 2022 The Authors
Divisions: Statistics
Subjects: H Social Sciences > HA Statistics
Date Deposited: 08 Apr 2022 15:18
Last Modified: 12 Jun 2022 18:03

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