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Compact hypothesis and extremal set estimators

2023; Volume: 23; Issue: 2 Linguagem: Inglês

10.7151/dmps.1039

2084-0381

João T. Mexia, Pedro Corte Real,

Statistical Methods and Inference

In extremal estimation theory the estimators are local or absolute extremes of functions defined on the cartesian product of the parameter by the sample space.Assuming that these functions converge uniformly, in a convenient stochastic way, to a limit function g, set estimators for the set ∇ of absolute maxima (minima) of g are obtained under the compactness assumption that ∇ is contained in a known compact U .A strongly consistent test is presented for this assumption.Moreover, when the true parameter value β k 0 is the sole point in ∇, strongly consistent pointwise estimators, { ˆ β k n : n ∈ N} for β k 0 are derived and confidence ellipsoids for β k 0 centered at ˆ β k n are obtained, as well as, strongly consistent tests.Lastly an application to binary data is presented.