caa a22 4500 47706289X CHVBK 20180405111405.0 cr unu---uuuuu 170330e19960901xx s 000 0 eng 10.1007/BF00050850 doi (NATIONALLICENCE)springer-10.1007/BF00050850 On sequential fixed-width confidence intervals for the mean and second-order expansions of the associated coverage probabilities [Elektronische Daten] [Nitis Mukhopadhyay, Sujay Datta] In order to construct fixed-width (2d) confidence intervals for the mean of an unknown distribution function F, a new purely sequential sampling strategy is proposed first. The approach is quite different from the more traditional methodology of Chow and Robbins (1965, Ann. Math. Statist., 36, 457-462). However, for this new procedure, the coverage probability is shown (Theorem 2.1) to be at least (1-α)+Ad 2+o(d2) as d→0 where (1-α) is the preassigned level of confidence and A is an appropriate functional of F, under some regularity conditions on F. The rates of convergence of the coverage probability to (1-α) obtained by Csenki (1980, Scand. Actuar. J., 107-111) and Mukhopadhyay (1981, Comm. Statist. Theory Methods, 10, 2231-2244) were merely O(d1/2-q), with 0<q<1/2, under the Chow-Robbins stopping time τ*. It is to be noted that such considerable sharpening of the rate of convergence of the coverage probability is achieved even though the new stopping variable is Op(τ*). An accelerated version of the stopping rule is also provided together with the analogous second-order characteristics. In the end, an example is given for the mean estimation problem of an exponential distribution. Kluwer Academic Publishers, 1996 Distribution-free nationallicence fixed-width confidence intervals nationallicence confidence level nationallicence second-order expansions nationallicence purely sequential nationallicence accelerated sequential nationallicence Markov inequality nationallicence Mukhopadhyay Nitis Department of Statistics, University of Connecticut, 06269, Storrs, CT, U.S.A. aut Datta Sujay Department of Statistics, University of Connecticut, 06269, Storrs, CT, U.S.A. aut Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 48/3(1996-09-01), 497-507 0020-3157 48:3<497 1996 48 10463 https://doi.org/10.1007/BF00050850 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00050850 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Mukhopadhyay Nitis Department of Statistics, University of Connecticut, 06269, Storrs, CT, U.S.A aut NATIONALLICENCE 700 1- Datta Sujay Department of Statistics, University of Connecticut, 06269, Storrs, CT, U.S.A aut NATIONALLICENCE 773 0- Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 48/3(1996-09-01), 497-507 0020-3157 48:3<497 1996 48 10463 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer