Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
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Finite-Sample, Small-Dispersion Asymptotic Optimality of the Non-Linear Least Squares Estimator

  • So, Beong-Soo (Department of Statistics, Ewha Womens University, Seoul 120-750)
  • Published : 1995.12.01
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Abstract

We consider the following type of general semi-parametric non-linear regression model : $y_i = f_i(\theta) + \epsilon_i, i=1, \cdots, n$ where ${f_i(\cdot)}$ represents the set of non-linear functions of the unknown parameter vector $\theta' = (\theta_1, \cdots, \theta_p)$ and ${\epsilon_i}$ represents the set of measurement errors with unknown distribution. Under suitable finite-sample, small-dispersion asymptotic framework, we derive a general lower bound for the asymptotic mean squared error (AMSE) matrix of the Gauss-consistent estimator of $\theta$. We then prove the fundamental result that the general non-linear least squares estimator (NLSE) is an optimal estimator within the class of all regular Gauss-consistent estimators irrespective of the type of the distribution of the measurement errors.

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