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The Uniqueness of Extremum Estimation

Author

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  • Volker Krätschmer

Abstract

Let W denote a family of probability distributions with parameter space Τ, and WG be a subfamily of W depending on a mapping G:Θ -> Τ. Extremum estimations of the parameter vector ν ∈ Θ are considered. Some sufficient conditions are presented to ensure the uniqueness with probability one. As important applications, the maximum likelihood estimation in curved exponential families and nonlinear regression models with independent disturbances as well as the maximum likelihood estimation of the location and scale parameters of Gumbel distributions are treated.

Suggested Citation

  • Volker Krätschmer, 2006. "The Uniqueness of Extremum Estimation," SFB 649 Discussion Papers SFB649DP2006-080, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    • Handle: RePEc:hum:wpaper:sfb649dp2006-080
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    More about this item

    Keywords

    Extremum Estimation; Sard’s Theorem; Nonlinear Regression; Curved Exponential Families; Gumbel Distributions.;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions

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