Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic Distributions of High-Dimensional Distance Correlation
  Inference   Distance correlation has become an increasingly popular tool for detecting
the nonlinear dependence between a pair of potentially high-dimensional random
vectors. Most existing works have explored its asymptotic distributions under
the null hypothesis of independence between the two random vectors when only
the sample size or the dimensionality diverges. Yet its asymptotic null
distribution for the more realistic setting when both sample size and
dimensionality diverge in the full range remains largely underdeveloped. In
this paper, we fill such a gap and develop central limit theorems and
associated rates of convergence for a rescaled test statistic based on the
bias-corrected distance correlation in high dimensions under some mild
regularity conditions and the null hypothesis. Our new theoretical results
reveal an interesting phenomenon of blessing of dimensionality for
high-dimensional distance correlation inference in the sense that the accuracy
of normal approximation can increase with dimensionality. Moreover, we provide
a general theory on the power analysis under the alternative hypothesis of
dependence, and further justify the capability of the rescaled distance
correlation in capturing the pure nonlinear dependency under moderately high
dimensionality for a certain type of alternative hypothesis. The theoretical
results and finite-sample performance of the rescaled statistic are illustrated
with several simulation examples and a blockchain application.

21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
3
The categories of this paper are: physics
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio