Parametric-Rate Inference for One-Sided Differentiable Parameters

Alexander R. Luedtke and Mark J. van der Laan

Journal of the American Statistical Association, 2018, vol. 113, issue 522, 780-788

Abstract: 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$\sqrt{n}$, 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.

Date: 2018
References: Add references at CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/01621459.2017.1285777 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:jnlasa:v:113:y:2018:i:522:p:780-788

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/UASA20

DOI: 10.1080/01621459.2017.1285777

Access Statistics for this article

Journal of the American Statistical Association is currently edited by Xuming He, Jun Liu, Joseph Ibrahim and Alyson Wilson

More articles in Journal of the American Statistical Association from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().