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The EFM approach for single-index models by Cui, Xia; Härdle, Wolfgang Karl; Zhu, Lixing is a scholarly article available to read on EtoBox.

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Single-index models are natural extensions of linear models and circumvent the so-called curse of dimensionality. They are becoming increasingly popular in many scientific fields including biostatistics, medicine, economics and financial econometrics. Estimating and testing the model index coefficients $\bolds{\beta}$ is one of the most important objectives in the statistical analysis. However, the commonly used assumption on the index coefficients, $\|\bolds{\beta}\|=1$, represents a nonregular problem: the true index is on the boundary of the unit ball. In this paper we introduce the EFM approach, a method of estimating functions, to study the single-index model. The procedure is to first relax the equality constraint to one with (d-1) components of $\bolds{\beta}$ lying in an open unit ball, and then to construct the associated (d-1) estimating functions by projecting the score function to the linear space spanned by the residuals with the unknown link being estimated by kernel estimating functions. The root-n consistency and asymptotic normality for the estimator obtained from solving the resulting estimating equations are achieved, and a Wilks type theorem for testing the inde

Author

Cui, Xia; Härdle, Wolfgang Karl; Zhu, Lixing

Published

2012

Language

EN