This analysis reveals the central limit theory for Hotelling’s T squared statistic using dimensionality reduction, highlighting implications for statistical inference.
In this paper, we use dimensional reduction technique to study the central limit theory (CLT) of Hotelling’s [Formula: see text] statistic. Specifically, we use a matrix denoted by [Formula: see text], to map [Formula: see text]-dimensional sample vectors to a [Formula: see text] dimensional subspace, where [Formula: see text] or [Formula: see text]. Under the condition of [Formula: see text] as [Formula: see text], we obtain the CLT of Hotelling’s [Formula: see text] statistic. Moreover, the selection of [Formula: see text] is also considered, which demonstrates good performance in the simulation studies.
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Yang et al. (2026) studied this question.
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