Some limiting theorems of some random quadratic forms

In this paper, the random quadratic form s 1 T ( S 1 D 1 S 1 T + σ 2 I ) - 1 s 1 is considered. The main motivation comes from the application to wireless communication. For τ > 0 , it is shown that s 1 T ( S 1 D 1 S 1 T + σ 2 I ) - 1 s 1 converges to a fixed quantity with convergence rate o a ....

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Bibliographic Details
Published in:Statistics & probability letters 2005-12, Vol.75 (3), p.151-157
Main Authors: Pan, Guangming, Miao, Boqi, Jin, Baisuo
Format: Article
Language:English
Subjects:
Applications
Convergence rate
Convergence rate Large dimensional matrix Martingale Quadratic forms
Exact sciences and technology
Insurance, economics, finance
Large dimensional matrix
Limit theorems
Martingale
Mathematics
Probability and statistics
Probability theory and stochastic processes
Quadratic forms
Sciences and techniques of general use
Statistics
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Summary:In this paper, the random quadratic form s 1 T ( S 1 D 1 S 1 T + σ 2 I ) - 1 s 1 is considered. The main motivation comes from the application to wireless communication. For τ > 0 , it is shown that s 1 T ( S 1 D 1 S 1 T + σ 2 I ) - 1 s 1 converges to a fixed quantity with convergence rate o a . s ( N 1 / 2 - τ ). Also, convergence in probability is established.
ISSN:0167-7152
1879-2103
DOI:10.1016/j.spl.2005.07.005