Summary
A renewal theorem of the elementary type for some stopping times which arise from some statistical estimation problems has been established. It is applied to prove the asymptotic risk efficiency for the problem of estimating the mean when the loss function is a weighted sum of the squared error and the sample size, and the variance is unknown. It is also applied to verify a conjecture of Robbins and Siegmund (1974) on the evaluation of the variance of the estimator of the logarithm of the odds ratio for a sequential procedure.
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Research supported by NSF Grant MCS-79-05811-A01
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Chow, Y.S., Hsiung, C.A. & Yu, K.F. A renewal theorem and its applications to some sequential procedures. Z. Wahrscheinlichkeitstheorie verw Gebiete 64, 241–250 (1983). https://doi.org/10.1007/BF01844608
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DOI: https://doi.org/10.1007/BF01844608