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A multidimensional Newton-Raphson method and its applications to the existence of asymptotic Fn-estimators and their stochastic expansions

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  • Michel, R.

Abstract

Given a suitable function Fn we define a class of estimators called asymptotic Fn-estimators (i.e., estimators which approximate the solution of Fn([theta]) = 0). It is proved that this class is nonvoid if appropriate regularity conditions are fulfilled and if one has at hand a suitable initial estimator. Furthermore, it is shown that Fn-estimators admit a stochastic expansion (which enables to give results on asymptotic expansions for the distribution of these estimators).

Suggested Citation

  • Michel, R., 1977. "A multidimensional Newton-Raphson method and its applications to the existence of asymptotic Fn-estimators and their stochastic expansions," Journal of Multivariate Analysis, Elsevier, vol. 7(2), pages 235-248, June.
    • Handle: RePEc:eee:jmvana:v:7:y:1977:i:2:p:235-248
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