Properties of the inverse of a noncentral Wishart matrix
Properties of the inverse of a noncentral Wishart matrix
The inverse of a non-central Wishart matrix occurs in a variety of contexts inmultivariate statistical work, including instrumental variables (IV) regression, but there has been very little work on its properties. In this paper we first provide an expression for the expectation of the inverse of a non-central Wishart matrix, and then go on to do the same for a number of scalar-valued functions of the inverse. The main result is obtained by exploiting simple but powerful group-equivariance properties of the expectation map involved. Subsequent results exploit the consequences of other invariance properties.
Hillier, Grant
3423bd61-c35f-497e-87a3-6a5fca73a2a1
Kan, Raymond
4068dcb5-18f4-4e95-845c-88e5e458fcfa
Hillier, Grant
3423bd61-c35f-497e-87a3-6a5fca73a2a1
Kan, Raymond
4068dcb5-18f4-4e95-845c-88e5e458fcfa
Hillier, Grant and Kan, Raymond
(2021)
Properties of the inverse of a noncentral Wishart matrix.
Econometric Theory.
(In Press)
Abstract
The inverse of a non-central Wishart matrix occurs in a variety of contexts inmultivariate statistical work, including instrumental variables (IV) regression, but there has been very little work on its properties. In this paper we first provide an expression for the expectation of the inverse of a non-central Wishart matrix, and then go on to do the same for a number of scalar-valued functions of the inverse. The main result is obtained by exploiting simple but powerful group-equivariance properties of the expectation map involved. Subsequent results exploit the consequences of other invariance properties.
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ET-4180-Corrected-2
- Accepted Manuscript
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Accepted/In Press date: 4 April 2021
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Local EPrints ID: 448344
URI: http://eprints.soton.ac.uk/id/eprint/448344
ISSN: 0266-4666
PURE UUID: fc97b4b7-e26b-4a53-bf02-503ce4cfdd46
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Date deposited: 20 Apr 2021 16:34
Last modified: 17 Mar 2024 02:38
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Author:
Raymond Kan
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