Inference for Projection Parameters in Linear Regression: beyond d = o(n^1/2)
arXiv (Cornell University)(2023)
摘要
We consider the problem of inference for projection parameters in linear
regression with increasing dimensions. This problem has been studied under a
variety of assumptions in the literature. The classical asymptotic normality
result for the least squares estimator of the projection parameter only holds
when the dimension d of the covariates is of a smaller order than n^1/2,
where n is the sample size. Traditional sandwich estimator-based Wald
intervals are asymptotically valid in this regime. In this work, we propose a
bias correction for the least squares estimator and prove the asymptotic
normality of the resulting debiased estimator. Precisely, we provide an
explicit finite sample Berry Esseen bound on the Normal approximation to the
law of the linear contrasts of the proposed estimator normalized by the
sandwich standard error estimate. Our bound, under only finite moment
conditions on covariates and errors, tends to 0 as long as d = o(n^2/3) up
to the polylogarithmic factors. Furthermore, we leverage recent methods of
statistical inference that do not require an estimator of the variance to
perform asymptotically valid statistical inference and that leads to a sharper
miscoverage control compared to Wald's. We provide a discussion of how our
techniques can be generalized to increase the allowable range of d even
further.
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关键词
projection parameters,linear regression,inference
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