Effects of measurement error on a class of single-index varying coefficient regression models (original) (raw)

Abstract

This paper investigates the estimation in a class of single-index varying coefficient regression model when some covariates are contaminated with measurement errors. A bias-corrected least square procedure based on the observed data is proposed. By replacing the nonparametric single index part with a local linear approximation, an iterative algorithm for estimating the index parameter is proposed. More importantly, a special case is identified in which the naive procedure provides consistent estimates for the single index parameters. Large sample properties of the proposed estimators are established. The finite sample performance of the proposed estimators are evaluated by simulation studies.

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Acknowledgements

The authors would like to thank editors and reviewers for their constructive comments which greatly improve the presentation of the paper; Weixing Song’s research is supported by the grants from NSF DMS 1205276.

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Authors and Affiliations

1. College of Mathematics and Computer Sciences, Shanxi Normal University, Linfen, 041004, China
   Jianhong Shi & Qian Yang
2. Kansas State University, Manhattan, KS, 66503, USA
   Xiongya Li & Weixing Song

Authors

1. Jianhong Shi
2. Qian Yang
3. Xiongya Li
4. Weixing Song

Corresponding author

Correspondence toWeixing Song.

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Shi, J., Yang, Q., Li, X. et al. Effects of measurement error on a class of single-index varying coefficient regression models.Comput Stat 32, 977–1001 (2017). https://doi.org/10.1007/s00180-017-0726-2

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• Received: 14 January 2016
• Accepted: 05 April 2017
• Published: 20 April 2017
• Issue date: September 2017
• DOI: https://doi.org/10.1007/s00180-017-0726-2

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