Locally Most Powerful Sequentially Planned Tests in Continuous Time

Abstract

In this article we study the problem of finding a locally most powerful sequentially planned test in a one-sided sequentially planned testing problem for stochastic processes of the exponential class with continuous time parameter, thereby applying the theory of optimal sampling in continuous time (cf. Roters, 1995b 1997). The theory presented here extends the discrete-time results of Berk (1975) and Schmitz (1993).

Keywords:

• Bellman equation
• Control variable
• Heat equation
• Homogeneous Markov case
• Independent increments
• One-sided test
• Optimal stopping
• Sequentially planned probability ratio test
• Stationary increments
• Stochastic process

Subject Classifications:

• 62L10
• 62L15

ACKNOWLEDGMENTS

I am very grateful to several anonymous referees, an Associate Editor, and the Editor for several helpful comments and suggestions to improve the readability of the paper.

Notes

Recommended by Bennett Eisenberg