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Failure of asymptotic independence for SS-SN statistics under strong long-run correlation
Let $T^{(D)}_{n}(\alpha,\hat j_n)$ and $Q^{(D)}_{n}(\alpha)$ denote the $L_\infty$ -type and $L_2$ -type sample-splitting self-normalized (SS-SN) statistics, respectively. Suppose th…
Conjectureopenasymptotic-independence high-dimensional-statistics sample-splittingarXiv posted 2 days ago

Failure of asymptotic independence for SS-SN statistics under strong long-run correlation