A Lower Bound for the Bayes Risk for Testing Sequentially the Sign of the Drift Parameter of a Wiener Process.
MASSACHUSETTS INST OF TECH CAMBRIDGE STATISTICS CENTER
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Let xt be a Wiener process with drift micron and variance 1 per unit of time. For testing H micron less than or equal to 0 was A micron greater than 0 with the loss function micron if the wrong decision is made and 0 otherwise, c cost of observation per unit time and micron has a prior distribution which is normal with mean 0 and variance delta sub 0 to the 2nd power, the authors followed an idea of Bickel and Yahav to obtain a lower bound for the Bayes risk and showed that this lower bound is strict as delta sub 0 approaches limit of infinity for all c. Author
- Statistics and Probability