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Ann Inst Stat Math. 2012 Aug;64(4):751-764.

The efficiency of the second-order nonlinear least squares estimator and its extension.

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Department of Statistics, Texas A&M University, College Station, TX 77843, USA.


We revisit the second-order nonlinear least square estimator proposed in Wang and Leblanc (Anne Inst Stat Math 60:883-900, 2008) and show that the estimator reaches the asymptotic optimality concerning the estimation variability. Using a fully semiparametric approach, we further modify and extend the method to the heteroscedastic error models and propose a semiparametric efficient estimator in this more general setting. Numerical results are provided to support the results and illustrate the finite sample performance of the proposed estimator.


Heteroscedasticity; Moments; Second-order least squares estimator; Semiparametric methods

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