Parametric-Rate Inference for One-Sided Differentiable Parameters
提出一种在非正则情形下构建参数速率置信区间的方法，适用于最大化参数估计问题，并应用于高维相关性分析，计算复杂度为O(np)。
Suppose one has a collection of parameters indexed by a (possibly infinite dimensional) set. Given data generated from some distribution, the objective is to estimate the maximal parameter in this collection evaluated at the distribution that generated the data. This estimation problem is typically nonregular when the maximizing parameter is nonunique, and as a result standard asymptotic techniques generally fail in this case. We present a technique for developing parametric-rate confidence intervals for the quantity of interest in these nonregular settings. We show that our estimator is asymptotically efficient when the maximizing parameter is unique so that regular estimation is possible. We apply our technique to a recent example from the literature in which one wishes to report the maximal absolute correlation between a prespecified outcome and one of p predictors. The simplicity of our technique enables an analysis of the previously open case where p grows with sample size. Specifically, we only require that log p grows slower than n, where n is the sample size. We show that, unlike earlier approaches, our method scales to massive datasets: the point estimate and confidence intervals can be constructed in O(np) time. Supplementary materials for this article are available online.