On converging boundaries for the SPRT

Abstract

We develop a generalized recursive method to obtain error probabilities and the expected sample size for a truncated SPRT with converging boundaries. Using Wald's constant bounds, for IID normal observations, integer truncation points are obtained that guarantee actual error probabilities no worse than the desired probabilities. A simple relationship is established to predict the expected sample size. Anderson's converging boundaries are applied to a discrete observation process. It is found that some of these boundaries are conservative while others yield actual error probabilities that are higher than desired. Other converging boundaries are also considered.

Keywords:

• Converging boundaries
• error probabilities
• expected sample size
• truncated SPRT