Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rerandomization with Diminishing Covariate Imbalance and Diverging
  Number of Covariates   Completely randomized experiments have been the gold standard for drawing
causal inference because they can balance all potential confounding on average.
However, they can often suffer from unbalanced covariates for realized
treatment assignments. Rerandomization, a design that rerandomizes the
treatment assignment until a prespecified covariate balance criterion is met,
has recently got attention due to its easy implementation, improved covariate
balance and more efficient inference. Researchers have then suggested to use
the assignments that minimize the covariate imbalance, namely the optimally
balanced design. This has caused again the long-time controversy between two
philosophies for designing experiments: randomization versus optimal and thus
almost deterministic designs. Existing literature argued that rerandomization
with overly balanced observed covariates can lead to highly imbalanced
unobserved covariates, making it vulnerable to model misspecification. On the
contrary, rerandomization with properly balanced covariates can provide robust
inference for treatment effects while sacrificing some efficiency compared to
the ideally optimal design. In this paper, we show it is possible that, by
making the covariate imbalance diminishing at a proper rate as the sample size
increases, rerandomization can achieve its ideally optimal precision that one
can expect with perfectly balanced covariates while still maintaining its
robustness. In particular, we provide the sufficient and necessary condition on
the number of covariates for achieving the desired optimality. Our results rely
on a more dedicated asymptotic analysis for rerandomization. The derived theory
for rerandomization provides a deeper understanding of its large-sample
property and can better guide its practical implementation. Furthermore, it
also helps reconcile the controversy between randomized and optimal designs.

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The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
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The categories of this paper are: funct-an
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The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: physics
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The categories of this paper are: econ
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: cs
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The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph