A remark on moment-dependent phase transitions in high-dimensional Gaussian approximations. (English) Zbl 1543.60031
Summary: In this article, we study the critical growth rates of dimension below which Gaussian critical values can be used for hypothesis testing but beyond which they cannot. We are particularly interested in how these growth rates depend on the number of moments that the observations possess.
MSC:
| 60F05 | Central limit and other weak theorems |
| 62E17 | Approximations to statistical distributions (nonasymptotic) |
| 60F10 | Large deviations |
| 62G09 | Nonparametric statistical resampling methods |
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