{"title":"Comparison of Translation Experiments","authors":"E. Torgersen","doi":"10.1214/AOMS/1177692372","DOIUrl":"https://doi.org/10.1214/AOMS/1177692372","url":null,"abstract":"","PeriodicalId":50764,"journal":{"name":"Annals of Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1972-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82720525","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Asymptotic Approximations for the Probability that a Sum of Lattice Random Vectors Lies in a Convex Set","authors":"J. K. Yarnold","doi":"10.1214/AOMS/1177692389","DOIUrl":"https://doi.org/10.1214/AOMS/1177692389","url":null,"abstract":"","PeriodicalId":50764,"journal":{"name":"Annals of Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1972-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79342946","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Law of the Iterated Logarithm for the Range of Random Walk","authors":"N. Jain, W. Pruitt","doi":"10.1214/AOMS/1177692404","DOIUrl":"https://doi.org/10.1214/AOMS/1177692404","url":null,"abstract":"","PeriodicalId":50764,"journal":{"name":"Annals of Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1972-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75103642","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Coding Theorem for Stationary, Asymptotically Memoryless, Continuous-time Channels","authors":"T. Kadota, A. Wyner","doi":"10.1214/AOMS/1177692392","DOIUrl":"https://doi.org/10.1214/AOMS/1177692392","url":null,"abstract":"We give a mathematical definition of stationary, asymptotically memoryless, continuous-time channels, and prove a coding theorem and its converse for such channels.","PeriodicalId":50764,"journal":{"name":"Annals of Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1972-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75580088","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Error Estimates for the Weak Convergence to Certain Infinitely Divisible Laws","authors":"Thomas Hern","doi":"10.1214/AOMS/1177692391","DOIUrl":"https://doi.org/10.1214/AOMS/1177692391","url":null,"abstract":"","PeriodicalId":50764,"journal":{"name":"Annals of Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1972-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86171785","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On Estimation of Tail End Probabilities of the Sample Mean for Linear Stochastic Processes","authors":"K. Chanda","doi":"10.1214/AOMS/1177692402","DOIUrl":"https://doi.org/10.1214/AOMS/1177692402","url":null,"abstract":"","PeriodicalId":50764,"journal":{"name":"Annals of Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1972-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72460856","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Hitting Time Distributions for General Stochastic Processes","authors":"Dudley Paul Johnson","doi":"10.1214/AOMS/1177692408","DOIUrl":"https://doi.org/10.1214/AOMS/1177692408","url":null,"abstract":"It is the purpose of this paper to suggest, by a simple example, that the methods which have been so successful in the study of temporally homogeneous Markov processes can be applied equally successfully to general stochastic processes. Let i be a probability measure in the space Q, W) of all measures on the measurable space (Q, SW) of all functions wt) mapping R+ = (0, oo) into a measurable space (S, ?) where _ is the a-field generated by the events X,(wO) = w(t) C U C ? and where S is a separable compact space with Borel sets ?, and suppose that the continuous functions in Q have i-outer measure one. Let Tt, t C R+ be the semigroup of linear operators on (Q, ) defined by Tje(X1l C U1, *..., IXtn CUn) = [(Xt+tl C U1,***, Xt+tn C U.) and let Eu, U C ? be the resolution of the identity Eu M(A) = [(Xo C U, A). Let $ be the weak * closure over the continuous functions on the product topology of (Q, SW) of the linear subspace of (Q, S) which is generated by measures of the form Eun Ttn ... EU1 Tt1 i and let $+ be the set of all probability measures in O. Suppose now that T is the first exit time of X from the interior U of S and let g be a continuous function on the boundary U' of U. Let (* be the set of all linear functionals 0* on ( which are continuous in the weak * topology of O. Let Tt*o*o = O*Tto 0* C (* 0 D and G*0*0= limh oh-l[Th*0*0 00* e @ 0 e +","PeriodicalId":50764,"journal":{"name":"Annals of Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1972-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80451582","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Theorem on Obstructive Distributions","authors":"R. Wijsman","doi":"10.1214/AOMS/1177692407","DOIUrl":"https://doi.org/10.1214/AOMS/1177692407","url":null,"abstract":"","PeriodicalId":50764,"journal":{"name":"Annals of Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1972-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1214/AOMS/1177692407","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72443405","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Note on Fine and Tight Qualitative Probabilities","authors":"I. Niiniluoto","doi":"10.1214/AOMS/1177692390","DOIUrl":"https://doi.org/10.1214/AOMS/1177692390","url":null,"abstract":"","PeriodicalId":50764,"journal":{"name":"Annals of Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1972-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80844595","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Likelihood ratio tests for sequential k-decision problems","authors":"G. Lorden","doi":"10.1214/AOMS/1177692374","DOIUrl":"https://doi.org/10.1214/AOMS/1177692374","url":null,"abstract":"Sequential tests of separated hypotheses concerning the parameter θ of a Koopman-Darmois family are studied from the point of view of minimizing expected sample sizes pointwise in θ subject to error probability bounds. Sequential versions of the (generalized) likelihood ratio test are shown to exceed the minimum expected sample sizes by at most M log log α(-1) uniformly in θ, where α is the smallest error probability bound. The proof considers the likelihood ratio tests as ensembles of sequential probability ratio tests and compares them with alternative procedures by constructing alternative ensembles, applying a simple inequality of Wald and a new inequality of similar type. A heuristic approximation is given for the error probabilities of likelihood ratio tests, which provides an upper bound in the case of a normal mean.","PeriodicalId":50764,"journal":{"name":"Annals of Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1972-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88477271","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}