2006-12-11Buch DOI: 10.18452/4010
The Uniqueness of Extremum Estimation
Let W denote a family of probability distributions with parameter space G, and WG be a subfamily of W depending on a mapping G: Î˜ -> \"Î¤\". Extremum estimations of the parameter vector Î½ âˆˆ Î˜ 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 regressionmodels with independent disturbances as well as the maximum likelihood estimation of the location and scale parameters of Gumbel distributions are treated.
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