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Sequential estimation of linear models in three stages. (English) Zbl 0692.62067

Summary: The objective of this study is to extend the triple sampling methodologies to cover problems that arise in linear models. In particular, we aim to study the performance of triple sampling procedures, while controlling the risk of estimating some linear functions of means under the normality assumption. Both point as well as confidence interval estimation techniques are considered. We point out that the goal of controlling the estimation risk is reached in all cases. It is also shown analytically that triple sampling procedures have the same features of the one-by-one sequential sampling schemes.

MSC:

62L12 Sequential estimation
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References:

[1] Anscombe FJ (1953) Sequential estimation. J Roy Statist Soc Ser B 15:1–29
[2] Chow YS, Robbins H (1965) On the asymptotic theory of fixed width sequential confidence intervals for the mean. Ann Math Statist 36:457–462 · Zbl 0142.15601 · doi:10.1214/aoms/1177700156
[3] Cox DR (1952) Estimation by double sampling. Biometrika 39:217–227 · Zbl 0047.13206
[4] Hall P (1981) Asymptotic theory of triple sampling for sequential estimation of a mean. Ann Statist 9:1229–1238 · Zbl 0478.62068 · doi:10.1214/aos/1176345639
[5] Hamdy HI (1988) Remarks on the asymptotic theory of triple stage estimation of the normal mean. Scand J of Stat 15:303–310 · Zbl 0682.62017
[6] Hamdy HI, Mukhopadhyay N, Costanza MC, Son MS (1988) Triple stage point estimation for the exponential location parameter. Annals of the Institute of Statistical Mathematics 40:785–797 · Zbl 0675.62070 · doi:10.1007/BF00049432
[7] Holewijn PJ (1969) Note on Weyl’s criterion and the uniform distribution of independent random variables. Ann Math Statist 40:1124–1125 · Zbl 0176.47502 · doi:10.1214/aoms/1177697624
[8] Mukhopadhyay N, Hamdy HI, Al-Mahmeed M, Costanza MC (1987) Three-stage point estimation procedures for a normal mean. Sequential Analysis 6:21–36 · Zbl 0622.62082 · doi:10.1080/07474948708836114
[9] Robbins H (1959) Sequential estimation of the mean of a normal population. Probability and Statistics – The Harald Cramer Volume 235–245. Almquist and Wiksell, Uppsala, Sweden · Zbl 0095.13005
[10] Simons G (1968) On the cost of not knowing the variance when making a fixed-width interval estimation of the mean. Ann Math Statist 39:1946–1952 · Zbl 0187.15805 · doi:10.1214/aoms/1177698024
[11] Stein C (1945) A two-sample test for a linear hypothesis whose power is independent of the variance. Ann Math Statist 16:243–258 · Zbl 0060.30403 · doi:10.1214/aoms/1177731088
[12] Woodroofe M (1987) Asymptotically optimal sequential point estimation in three stages. In New Perspectives in Theoretical and Applied Statistics. John Wiley and Sons, Inc., New York, pp 397–411 · Zbl 0617.62086
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