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

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