Self-normalized Cram\'er Type Moderate Deviations under Dependence

摘要: We establish a Cram\'er-type moderate deviation result for self-normalized sums of weakly dependent random variables, where the moment requirement is much weaker than non-self-normalized counterpart. The range shown to depend on condition and degree dependence underlying processes. consider two types self-normalization: big-block-small-block scheme interlacing or equal-block scheme. Simulation study shows that latter can have better finite-sample performance. Our applied multiple testing construction simultaneous confidence intervals high-dimensional time series mean vectors.