Random Walk and Renewal Theory
Wald’s approximations to the power function and expected sample size of a sequential probability ratio test are based on ignoring the discrepancy between the (log) likelihood ratio and the stopping boundary, thus replacing a random variable by a constant. In what follows we develop methods to approximate this discrepancy and hence to obtain more accurate results. Some of the approximations have already been stated and used in III.5 and IV.3. The present chapter is concerned with linear stopping boundaries; and the more difficult non-linear case is discussed in Chapter IX. An alternative method for linear problems is given in Chapter X.
KeywordsExponential Family Normal Random Variable Renewal Theory Sequential Probability Ratio Test Renewal Theorem
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