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- Title
Modal non‐linear regression in the presence of Laplace measurement error.
- Authors
Shi, Jianhong; Zhang, Jie; Wang, Xiaorui; Song, Weixing
- Abstract
Summary: In this paper, we propose a robust estimation procedure for a class of non‐linear regression models when the covariates are contaminated with Laplace measurement error, aiming at constructing an estimation procedure for the regression parameters which are less affected by the possible outliers, and heavy‐tailed underlying distribution, as well as reducing the bias introduced by the measurement error. Starting with the modal regression procedure developed for the measurement error‐free case, a non‐trivial modification is made so that the modified version can effectively correct the potential bias caused by measurement error. Large sample properties of the proposed estimate, such as the convergence rate and the asymptotic normality, are thoroughly investigated. A simulation study and real data application are conducted to illustrate the satisfying finite sample performance of the proposed estimation procedure. A modal estimation procedure is proposed for nonlinear regression models when the covariates are measured with Laplace error. It enjoys the merits of both robustness and bias reduction.
- Subjects
MEASUREMENT errors; LAPLACE distribution; NONLINEAR regression; ASYMPTOTIC normality; REGRESSION analysis
- Publication
Australian & New Zealand Journal of Statistics, 2020, Vol 62, Issue 2, p232
- ISSN
1369-1473
- Publication type
Article
- DOI
10.1111/anzs.12291