Compact hypothesis and extremal set estimators

João Tiago Mexia; Pedro Corte Real

Discussiones Mathematicae Probability and Statistics (2003)

  • Volume: 23, Issue: 2, page 103-121
  • ISSN: 1509-9423

Abstract

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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 ₀ → k is the sole point in ∇, strongly consistent pointwise estimators, k : n ∈ ℕ for β ₀ → k are derived and confidence ellipsoids for β ₀ → k centered at k are obtained, as well as, strongly consistent tests. Lastly an application to binary data is presented.

How to cite

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João Tiago Mexia, and Pedro Corte Real. "Compact hypothesis and extremal set estimators." Discussiones Mathematicae Probability and Statistics 23.2 (2003): 103-121. <http://eudml.org/doc/287599>.

@article{JoãoTiagoMexia2003,
abstract = {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 $\vec\{β₀\}^\{k\}$ is the sole point in ∇, strongly consistent pointwise estimators, $\{ ^\{k\}: n ∈ ℕ \}$ for $\vec\{β₀\}^\{k\}$ are derived and confidence ellipsoids for $\vec\{β₀\}^\{k\}$ centered at $^\{k\}$ are obtained, as well as, strongly consistent tests. Lastly an application to binary data is presented.},
author = {João Tiago Mexia, Pedro Corte Real},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {extremal estimators; set estimators; confidence ellipsoids; strong consistency; binary data; pseudo maximum likelihood},
language = {eng},
number = {2},
pages = {103-121},
title = {Compact hypothesis and extremal set estimators},
url = {http://eudml.org/doc/287599},
volume = {23},
year = {2003},
}

TY - JOUR
AU - João Tiago Mexia
AU - Pedro Corte Real
TI - Compact hypothesis and extremal set estimators
JO - Discussiones Mathematicae Probability and Statistics
PY - 2003
VL - 23
IS - 2
SP - 103
EP - 121
AB - 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 $\vec{β₀}^{k}$ is the sole point in ∇, strongly consistent pointwise estimators, ${ ^{k}: n ∈ ℕ }$ for $\vec{β₀}^{k}$ are derived and confidence ellipsoids for $\vec{β₀}^{k}$ centered at $^{k}$ are obtained, as well as, strongly consistent tests. Lastly an application to binary data is presented.
LA - eng
KW - extremal estimators; set estimators; confidence ellipsoids; strong consistency; binary data; pseudo maximum likelihood
UR - http://eudml.org/doc/287599
ER -

References

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