A Simple Asymptotic Bound on the Error of the Ordinary Normal Approximation to the Student's t-Distribution

A simple asymptotic bound on the error of the ordinary normal approximation (ONA) to the Student's t-distribution is derived. The proposed bound provides a quick calculation of the minimum number of degrees of freedom required to ensure a given approximation error. Then, the application of the...

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Bibliographic Details
Published in:IEEE communications letters 2015-08, Vol.19 (8), p.1295-1298
Main Authors: Shafiei, Akbar, Saberali, S. Mohammad
Format: Article
Language:English
Subjects:
Accuracy
Approximation error
Confidence interval
detection theory
Electrical engineering
Maximum likelihood estimation
ordinary normal approximation (ONA)
Random variables
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Summary:A simple asymptotic bound on the error of the ordinary normal approximation (ONA) to the Student's t-distribution is derived. The proposed bound provides a quick calculation of the minimum number of degrees of freedom required to ensure a given approximation error. Then, the application of the ONA is investigated in confidence interval determination and detection theory. Finally, using the proposed bound, further simple bounds on the approximation error of the confidence level and the false-alarm probability are obtained.
ISSN:1089-7798
1558-2558
DOI:10.1109/LCOMM.2015.2442576