Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $L^2$ Asymptotics for High-Dimensional Data   We develop an asymptotic theory for $L^2$ norms of sample mean vectors of
high-dimensional data. An invariance principle for the $L^2$ norms is derived
under conditions that involve a delicate interplay between the dimension $p$,
the sample size $n$ and the moment condition. Under proper normalization,
central and non-central limit theorems are obtained. To facilitate the related
statistical inference, we propose a plug-in calibration method and a
re-sampling procedure to approximate the distributions of the $L^2$ norms. Our
results are applied to multiple tests and inference of covariance matrix
structures.

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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: cs
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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
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The categories of this paper are: plasm-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex