SIMEX estimation for single-index model with covariate measurement error

Yiping Yang, Tiejun Tong and Gaorong Li ()
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Yiping Yang: Chongqing Technology and Business University
Tiejun Tong: Hong Kong Baptist University
Gaorong Li: Beijing University of Technology

AStA Advances in Statistical Analysis, 2019, vol. 103, issue 1, No 6, 137-161

Abstract: Abstract In this paper, we consider the single-index measurement error model with mismeasured covariates in the nonparametric part. To solve the problem, we develop a simulation-extrapolation (SIMEX) algorithm based on the local linear smoother and the estimating equation. For the proposed SIMEX estimation, it is not needed to assume the distribution of the unobserved covariate. We transform the boundary of a unit ball in $${\mathbb {R}}^p$$ R p to the interior of a unit ball in $${\mathbb {R}}^{p-1}$$ R p - 1 by using the constraint $$\Vert \beta \Vert =1$$ ‖ β ‖ = 1 . The proposed SIMEX estimator of the index parameter is shown to be asymptotically normal under some regularity conditions. We also derive the asymptotic bias and variance of the estimator of the unknown link function. Finally, the performance of the proposed method is examined by simulation studies and is illustrated by a real data example.

Keywords: Single-index model; Measurement error; Local linear smoother; SIMEX; Estimating equation; Primary 62G05; 62G08; Secondary 62G20 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s10182-018-0327-6

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