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On the limit properties of maximal likelihood estimators in a Hilbert space
-
Petre Babilua
,
Elizbar Nadaraya
Published/Copyright:
April 14, 2015
Abstract
We develop the method of maximal likelihood for infinite-dimensional Hilbert spaces and prove several theorems about consistency and asymptotic normality.
Keywords: Maximum likelihood estimation; infinite dimensional spaces; consistency; asymptotical normality
Funding source: Shota Rustaveli National Scientific Foundation
Award Identifier / Grant number: FR/308/5-104/12
The authors would like to thank the referees for their careful and thorough reading of the paper.
Received: 2013-10-15
Revised: 2014-4-4
Accepted: 2014-12-15
Published Online: 2015-4-14
Published in Print: 2015-6-1
© 2015 by De Gruyter
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Articles in the same Issue
- Frontmatter
- I2(u)-convergence of double sequences of order (α,β)
- Regular elements of the complete semigroups of binary relations of the class Σ6(X,8)
- On the limit properties of maximal likelihood estimators in a Hilbert space
- Shadowing and average shadowing properties for iterated function systems
- On almost increasing and quasi monotone sequences
- An unabelian version of the Voronov higher bracket construction
- Necessary and sufficient conditions for the ℍ-differentiability of quaternion functions
- k-step nilpotent Lie algebras
- An optimal control problem for a system of linear hyperbolic differential equations with constant coefficients
- On topologies in the family of sets with the Baire property
- On some inequalities for functions whose absolute values of the second derivatives are α-, m-, (α,m)-logarithmically convex
- On the cardinalities of at-sets in a real Hilbert space
- Higher-order Bernoulli and poly-Bernoulli mixed type polynomials
- On the existence of solutions for nonlocal boundary value problems
- fpn-injective and fpn-flat modules
- Algebroid functions with given Borel points
Keywords for this article
Maximum likelihood estimation;
infinite dimensional spaces;
consistency;
asymptotical normality
Articles in the same Issue
- Frontmatter
- I2(u)-convergence of double sequences of order (α,β)
- Regular elements of the complete semigroups of binary relations of the class Σ6(X,8)
- On the limit properties of maximal likelihood estimators in a Hilbert space
- Shadowing and average shadowing properties for iterated function systems
- On almost increasing and quasi monotone sequences
- An unabelian version of the Voronov higher bracket construction
- Necessary and sufficient conditions for the ℍ-differentiability of quaternion functions
- k-step nilpotent Lie algebras
- An optimal control problem for a system of linear hyperbolic differential equations with constant coefficients
- On topologies in the family of sets with the Baire property
- On some inequalities for functions whose absolute values of the second derivatives are α-, m-, (α,m)-logarithmically convex
- On the cardinalities of at-sets in a real Hilbert space
- Higher-order Bernoulli and poly-Bernoulli mixed type polynomials
- On the existence of solutions for nonlocal boundary value problems
- fpn-injective and fpn-flat modules
- Algebroid functions with given Borel points
