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June 2020 On post dimension reduction statistical inference
Kyongwon Kim, Bing Li, Zhou Yu, Lexin Li
Ann. Statist. 48(3): 1567-1592 (June 2020). DOI: 10.1214/19-AOS1859

Abstract

The methodologies of sufficient dimension reduction have undergone extensive developments in the past three decades. However, there has been a lack of systematic and rigorous development of post dimension reduction inference, which has seriously hindered its applications. The current common practice is to treat the estimated sufficient predictors as the true predictors and use them as the starting point of the downstream statistical inference. However, this naive inference approach would grossly overestimate the confidence level of an interval, or the power of a test, leading to the distorted results. In this paper, we develop a general and comprehensive framework of post dimension reduction inference, which can accommodate any dimension reduction method and model building method, as long as their corresponding influence functions are available. Within this general framework, we derive the influence functions and present the explicit post reduction formulas for the combinations of numerous dimension reduction and model building methods. We then develop post reduction inference methods for both confidence interval and hypothesis testing. We investigate the finite-sample performance of our procedures by simulations and a real data analysis.

Citation

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Kyongwon Kim. Bing Li. Zhou Yu. Lexin Li. "On post dimension reduction statistical inference." Ann. Statist. 48 (3) 1567 - 1592, June 2020. https://doi.org/10.1214/19-AOS1859

Information

Received: 1 August 2018; Revised: 1 April 2019; Published: June 2020
First available in Project Euclid: 17 July 2020

zbMATH: 07241603
MathSciNet: MR4124335
Digital Object Identifier: 10.1214/19-AOS1859

Subjects:
Primary: 62G08
Secondary: 62H99

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.48 • No. 3 • June 2020
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