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2015 Oracally efficient estimation for single-index link function with simultaneous confidence band
Lijie Gu, Lijian Yang
Electron. J. Statist. 9(1): 1540-1561 (2015). DOI: 10.1214/15-EJS1051

Abstract

Over the last twenty-five years, various $\sqrt{n}$-consistent estimators have been devised for the coefficient vector in the popular semiparametric single-index model. In this paper, we prove under general assumptions that the kernel estimator of the link function by a univariate regression on the index variable is oracally efficient, namely, the estimator with the true single-index coefficient vector is asymptotically indistinguishable from that with any $\sqrt{n}$-consistent coefficient vector estimator. As a mathematical byproduct of the oracle efficiency, a simultaneous confidence band is constructed for the link function based on the oracally efficient kernel estimator. Simulation experiments corroborate the theoretical results. The proposed simultaneous confidence band is applied to analyze and test hypothesis about the Boston housing data.

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Lijie Gu. Lijian Yang. "Oracally efficient estimation for single-index link function with simultaneous confidence band." Electron. J. Statist. 9 (1) 1540 - 1561, 2015. https://doi.org/10.1214/15-EJS1051

Information

Received: 1 January 2015; Published: 2015
First available in Project Euclid: 23 July 2015

zbMATH: 1327.62254
MathSciNet: MR3376116
Digital Object Identifier: 10.1214/15-EJS1051

Subjects:
Primary: 62G08
Secondary: 62G15

Rights: Copyright © 2015 The Institute of Mathematical Statistics and the Bernoulli Society

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Vol.9 • No. 1 • 2015
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