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Structure of sequential tests minimizing an expected sample size. (English) Zbl 0407.62055

##### MSC:
 62L10 Sequential statistical analysis
Full Text:
##### References:
 [1] Anderson, T.W.: A modification of the sequential probability ratio test to reduce the sample size. Ann. Math. Statist.31, 165-197 (1960) · Zbl 0089.35501 [2] Burkholder, D.L., Wijsman, R.A.: Optimum properties and admissibility of sequential tests. Ann. Math. Statist.34, 1-17 (1963) · Zbl 0113.13005 [3] Chow, Y.S., Robbins, H., Siegmund, D.: Great Expectations: The Theory of Optimal Stopping. Boston: Houghton-Mifflin 1971 · Zbl 0233.60044 [4] Ferguson, T.S.: Mathematical Statistics, a Decision Theoretic Approach. New York: Academic Press 1967 · Zbl 0153.47602 [5] Kiefer, J., Weiss, L.: Some properties of generalized sequential probability ratio tests. Ann. Math. Statist.28, 57-75 (1957) · Zbl 0079.35406 [6] Lai, T.L.: Optimal stopping and sequential tests which minimize the maximum expected sample size. Ann. Statist.1, 659-673 (1973) · Zbl 0261.62062 [7] Lehmann, E.L.: Testing Statistical Hypotheses. New York: Wiley 1959 · Zbl 0089.14102 [8] Lorden, G.: 2-SPRT’s and the modified Kiefer-Weiss problem of minimizing an expected sample size. Ann. Statist.4, 281-291 (1976) · Zbl 0367.62099 [9] Lorden, G.: Nearly-optimal sequential tests for finitely many parameter values. Ann. Statist.5, 1-21 (1977) · Zbl 0386.62070 [10] Matthes, T.K.: On the optimality of sequential probability ratio tests. Ann. Math. Statist.34, 18-21 (1963) · Zbl 0113.13102 [11] Simons, G.: An improved statement of optimality for sequential probability ratio tests. Ann. Statist.4, 1240-1243 (1976) · Zbl 0346.62059 [12] Spitzer, F.: A combinatorial lemma and its application to probability theory. Trans. Amer. Math. Soc.82, 332-339 (1956) · Zbl 0071.13003 [13] Wald, A., Wolfowitz, J.: Optimum character of the sequential probability ratio test. Ann. Math. Statist.19, 326-339 (1948) · Zbl 0032.17302 [14] Weiss, L.: On sequential tests which minimize the maximum expected sample size. J. Amer. Statist. Assoc.57, 551-566 (1962) · Zbl 0114.10304 [15] Wijsman, R.A.: Existence, uniqueness, and monotonicity of sequential probability ratio tests. Ann. Math. Statist.34, 1541-1548 (1963) · Zbl 0212.21101
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