×
Bartroff, Jay

Asymptotically optimal multistage tests of simple hypotheses. (English) Zbl 1126.62066

Ann. Stat. 35, No. 5, 2075-2105 (2007).
Summary: A family of variable stage size multistage tests of simple hypotheses is described, based on efficient multistage sampling procedures. Using a loss function that is a linear combination of sampling costs and error probabilities, these tests are shown to minimize the integrated risk to second order as the costs per stage and per observation approach zero. A numerical study shows significant improvement over group sequential tests in a binomial testing problem.

Cited in 5 Documents

MSC:

62L10 Sequential statistical analysis
62F05 Asymptotic properties of parametric tests

Keywords:

multistage; hypothesis testing; asymptotic optimality; group sequential
Cite Review PDF
Full Text: DOI arXiv Euclid

References:

[1] Barber, S. and Jennison, C. (2002). Optimal asymmetric one-sided group sequential tests. Biometrika 89 49–60. JSTOR: · Zbl 0998.62067 · doi:10.1093/biomet/89.1.49
[2] Bartroff, J. (2004). Asymptotically optimal multistage hypothesis tests . Ph.D. dissertation, Caltech. · Zbl 1126.62066
[3] Bartroff, J. (2006). Optimal multistage sampling in a boundary-crossing problem. Sequential Anal. 25 59–84. · Zbl 1085.62094 · doi:10.1080/07474940500452247
[4] Chernoff, H. (1961). Sequential tests for the mean of a normal distribution. Proc. Fourth Berkeley Symp. Math. Statist. Probab. 1 79–91. Univ. California Press, Berkeley. · Zbl 0133.11904
[5] Cressie, N. and Morgan, P. B. (1993). The VPRT: A sequential testing procedure dominating the SPRT. Econometric Theory 9 431–450. JSTOR:
[6] Durrett, R. (1995). Probability : Theory and Examples , 2nd ed. Duxburry, Belmont, CA. · Zbl 1202.60001
[7] Eales, J. D. and Jennison, C. (1992). An improved method for deriving optimal one-sided group sequential tests. Biometrika 79 13–24. JSTOR: · Zbl 0850.62633 · doi:10.1093/biomet/79.1.13
[8] Eales, J. D. and Jennison, C. (1995). Optimal two-sided group sequential tests. Sequential Anal. 14 273–286. · Zbl 0838.62064 · doi:10.1080/07474949508836337
[9] Feller, W. (1971). An Introduction to Probability Theory and Its Applications 2 , 2nd ed. Wiley, New York. · Zbl 0219.60003
[10] Hall, P. (1982). Rates of Convergence in the Central Limit Theorem . Pitman, Boston. · Zbl 0497.60001
[11] Jennison, C. and Turnbull, B. W. (2000). Group Sequential Methods with Applications to Clinical Trials . Chapman and Hall/CRC, Boca Raton, FL. · Zbl 0934.62078
[12] Kim, K. and DeMets, D. L. (1987). Design and analysis of group sequential tests based on the type I error spending rate function. Biometrika 74 149–154. JSTOR: · Zbl 0613.62103 · doi:10.1093/biomet/74.1.149
[13] Lai, T. L. and Shih, M.-C. (2004). Power, sample size and adaptation considerations in the design of group sequential clinical trials. Biometrika 91 507–528. · Zbl 1113.62090 · doi:10.1093/biomet/91.3.507
[14] Lorden, G. (1967). Integrated risk of asymptotically Bayes sequential tests. Ann. Math. Statist. 38 1399–1422. · Zbl 0171.16602 · doi:10.1214/aoms/1177698696
[15] Lorden, G. (1976). 2-SPRT’s and the modified Kiefer–Weiss problem of minimizing an expected sample size. Ann. Statist. 4 281–291. · Zbl 0367.62099 · doi:10.1214/aos/1176343407
[16] Lorden, G. (1977). Nearly-optimal sequential tests for finitely many parameter values. Ann. Statist. 5 1–21. · Zbl 0386.62070 · doi:10.1214/aos/1176343737
[17] Lorden, G. (1983). Asymptotic efficiency of three-stage hypothesis tests. Ann. Statist. 11 129–140. · Zbl 0519.62022 · doi:10.1214/aos/1176346064
[18] Morgan, P. B. and Cressie, N. (1997). A comparison of the cost-efficiencies of the sequential, group-sequential and variable-sample-size-sequential probability ratio tests. Scand. J. Statist. 24 181–200. · Zbl 0885.62093 · doi:10.1111/1467-9469.00057
[19] Pocock, S. J. (1982). Interim analyses for randomized clinical trials: The group sequential approach. Biometrics 38 153–162.
[20] Schmitz, N. (1993). Optimal Sequentially Planned Decision Procedures . Lecture Notes in Statist. 79 . Springer, New York. · Zbl 0771.62057
[21] Wang, S. K. and Tsiatis, A. A. (1987). Approximately optimal one-parameter boundaries for group sequential trials. Biometrics 43 193–199. JSTOR: · Zbl 0609.62120 · doi:10.2307/2531959
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.