On sequential fixed-width confidence intervals for the mean and second-order expansions of the associated coverage probabilities
dc.contributor.author | Mukhopadhyay, Nitis | en_US |
dc.contributor.author | Datta, Sujay | en_US |
dc.date.accessioned | 2006-09-11T19:35:39Z | |
dc.date.available | 2006-09-11T19:35:39Z | |
dc.date.issued | 1996-09 | en_US |
dc.identifier.citation | Mukhopadhyay, Nitis; Datta, Sujay; (1996). "On sequential fixed-width confidence intervals for the mean and second-order expansions of the associated coverage probabilities." Annals of the Institute of Statistical Mathematics 48(3): 497-507. <http://hdl.handle.net/2027.42/47956> | en_US |
dc.identifier.issn | 0020-3157 | en_US |
dc.identifier.issn | 1572-9052 | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/47956 | |
dc.description.abstract | 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 (d 2 ) 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 (d 1/2-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 O p (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. | en_US |
dc.format.extent | 602127 bytes | |
dc.format.extent | 3115 bytes | |
dc.format.mimetype | application/pdf | |
dc.format.mimetype | text/plain | |
dc.language.iso | en_US | |
dc.publisher | Kluwer Academic Publishers; The Institute of Statistical Mathematics ; Springer Science+Business Media | en_US |
dc.subject.other | Purely Sequential | en_US |
dc.subject.other | Statistics, General | en_US |
dc.subject.other | Statistics | en_US |
dc.subject.other | Distribution-free | en_US |
dc.subject.other | Statistics for Business/Economics/Mathematical Finance/Insurance | en_US |
dc.subject.other | Second-order Expansions | en_US |
dc.subject.other | Accelerated Sequential | en_US |
dc.subject.other | Markov Inequality | en_US |
dc.subject.other | Confidence Level | en_US |
dc.subject.other | Fixed-width Confidence Intervals | en_US |
dc.title | On sequential fixed-width confidence intervals for the mean and second-order expansions of the associated coverage probabilities | en_US |
dc.type | Article | en_US |
dc.subject.hlbsecondlevel | Statistics and Numeric Data | en_US |
dc.subject.hlbsecondlevel | Mathematics | en_US |
dc.subject.hlbtoplevel | Social Sciences | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | Department of Statistics, University of Connecticut, 06269, Storrs, CT, U.S.A.; Department of Statistics, University of Michigan, 48109, Ann Arbor, MI, U.S.A. | en_US |
dc.contributor.affiliationother | Department of Statistics, University of Connecticut, 06269, Storrs, CT, U.S.A. | en_US |
dc.contributor.affiliationumcampus | Ann Arbor | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/47956/1/10463_2004_Article_BF00050850.pdf | en_US |
dc.identifier.doi | http://dx.doi.org/10.1007/BF00050850 | en_US |
dc.identifier.source | Annals of the Institute of Statistical Mathematics | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
Files in this item
Remediation of Harmful Language
The University of Michigan Library aims to describe library materials in a way that respects the people and communities who create, use, and are represented in our collections. Report harmful or offensive language in catalog records, finding aids, or elsewhere in our collections anonymously through our metadata feedback form. More information at Remediation of Harmful Language.
Accessibility
If you are unable to use this file in its current format, please select the Contact Us link and we can modify it to make it more accessible to you.