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We show that under different moment bounds on the underlying variables,
bootstrap approximation to the large deviation probabilities of
standardized sample sum, based on independent random variables, is valid
for a wider zone of n, the sample size, compared to the classical normal
tail probability approximation. As an application, different notions of
efficiency for statistical tests are considered from Bayesian point of
view. In particular, efficiency due to Pitman (1938), Chernoff (1952), and
Bayes risk efficiency due to Rubin and Sethuraman (1965) turn out to be
special cases with the choice of the weight function; i.e., prior density
times loss.
The technique is explained by a data example where two processes with
different levels of noise are considered. Such a situation is frequently
encountered in electronic recordings like EEG/ECG etc., where noise is
usually associated with signal.
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