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Sequential approach to simultaneous estimation of the mean and variance. (English) Zbl 0468.62078

##### MSC:
 62L12 Sequential estimation 62F10 Point estimation
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##### References:
 [1] Anscombe, F.J.: Large sample theory of sequential estimation. Proc. Camb. Phil. Soc.48, 1952, 600–607. · Zbl 0047.13401 [2] Chow, Y.S., andH. Robbins: On the asymptotic theory of fixed width sequential confidence intervals for the mean. Ann. Math. Statist.36, 1965, 457–462. · Zbl 0142.15601 [3] Mukhopadhyay, N.: Sequential Methods in estimation and prediction. Ph. D. Thesis, Indian Statistical Institute, 1976. · Zbl 0331.62062 [4] –: Remarks on sequential estimation of a linear function of two means: the normal case. Metrika24, 1977, 197–201. · Zbl 0368.62063 [5] Robbins, H.: Sequential estimation of mean of a normal population. Probability and Statistics (H. Cramer’s Volume). Uppsala 1959, 235–245. [6] Robbins, H., G. Simons, andN. Staar: A sequential analogue of the Behrens-Fisher problem. Ann. Math. Statist.38, 1967, 1384–1391. · Zbl 0157.48105 [7] Sproule, R.N.: Asymptotic properties ofU-statistics, Amer. Math. Soc. Transactions199, 1974, 55–64. · Zbl 0307.60028 [8] Srivastava, M.S.: On fixed width confidence bounds for regression parameters and mean vector. J. Roy. Stat. Soc., B29, 1967, 132–140. · Zbl 0152.37002 [9] –: On a sequential analogue of the Behrens-Fisher problem. J. Roy. Stat. Soc., B32, 1970, 144–148. · Zbl 0209.50404 [10] Starr, N.: On the asymptotic efficiency of a sequential procedure for estimating the mean. Ann. Math. Statist.37, 1966, 1173–1185. · Zbl 0144.40801 [11] Starr, N., andM. Woodroofe: Remarks on sequential point estimation. Proc. Nat. Acad. Sci. USA61, 1969, 285–288. · Zbl 0202.17304 [12] Stein, C.: A two sample test for a linear hypothesis whose power is independent of the variance. Ann. Math. Statist.16, 1945, 243–258. · Zbl 0060.30403 [13] Wiener, N.: The ergodic theorem. Duke J. Math.5, 1939, 1–18. · JFM 65.0516.04
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