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Nonlinear regression models with single‐index heteroscedasticity

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  • Jun Zhang
  • Yujie Gai
  • Bingqing Lin
  • Xuehu Zhu

Abstract

We consider nonlinear heteroscedastic single‐index models where the mean function is a parametric nonlinear model and the variance function depends on a single‐index structure. We develop an efficient estimation method for the parameters in the mean function by using the weighted least squares estimation, and we propose a “delete‐one‐component” estimator for the single‐index in the variance function based on absolute residuals. Asymptotic results of estimators are also investigated. The estimation methods for the error distribution based on the classical empirical distribution function and an empirical likelihood method are discussed. The empirical likelihood method allows for incorporation of the assumptions on the error distribution into the estimation. Simulations illustrate the results, and a real chemical data set is analyzed to demonstrate the performance of the proposed estimators.

Suggested Citation

  • Jun Zhang & Yujie Gai & Bingqing Lin & Xuehu Zhu, 2019. "Nonlinear regression models with single‐index heteroscedasticity," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 73(2), pages 292-316, May.
    • Handle: RePEc:bla:stanee:v:73:y:2019:i:2:p:292-316
    DOI: 10.1111/stan.12170
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    Cited by:

    1. Jun Zhang & Yiping Yang & Gaorong Li, 2020. "Logarithmic calibration for multiplicative distortion measurement errors regression models," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 74(4), pages 462-488, November.

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