On Sampling Moments of Nonlinear Estimators.
WISCONSIN UNIV MADISON DEPT OF STATISTICS
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In the paper the approximate sampling moments of least squares estimators in nonlinear models under the usual assumptions about the normality of the errors are obtained by expanding the normal equations in a Taylor series about the true values of the parameters. The expanded equations are then formally inverted and appropriate expectations taken in order to obtain the desired moments in terms of the higher derivatives of the model with respect to the parameters. Formulas, correct to order N sup-4, are given for the first six moments of the sampling distribution of one nonlinear parameter. The analogous first term in the bias for the multi-parameter case is also given. A numerical example is provided for the one parameter case. Author
- Statistics and Probability