{"title":"Bivariate Tests for Location and Their Bahadur Efficiencies","authors":"T. Killeen, T. Hettmansperger","doi":"10.1214/AOMS/1177692383","DOIUrl":"https://doi.org/10.1214/AOMS/1177692383","url":null,"abstract":"","PeriodicalId":50764,"journal":{"name":"Annals of Mathematical Statistics","volume":"40 1","pages":"1507-1516"},"PeriodicalIF":0.0,"publicationDate":"1972-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86419440","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":"Non-Optimality of Preliminary-Test Estimators for the Mean of a Multivariate Normal Distribution","authors":"S. Sclove, C. Morris, R. Radhakrishnan","doi":"10.1214/AOMS/1177692380","DOIUrl":"https://doi.org/10.1214/AOMS/1177692380","url":null,"abstract":"","PeriodicalId":50764,"journal":{"name":"Annals of Mathematical Statistics","volume":"28 1","pages":"1481-1490"},"PeriodicalIF":0.0,"publicationDate":"1972-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82213093","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 Representation of Independent Increment Processes without Gaussian Components","authors":"T. Ferguson, M. Klass","doi":"10.1214/AOMS/1177692395","DOIUrl":"https://doi.org/10.1214/AOMS/1177692395","url":null,"abstract":"","PeriodicalId":50764,"journal":{"name":"Annals of Mathematical Statistics","volume":"54 67 1","pages":"1634-1643"},"PeriodicalIF":0.0,"publicationDate":"1972-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80594123","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}
Abstract : The paper characterizes (1) the class of functions which lead to a total ordering of a class of experiments and (2) the class of transformations of a function Y which preserve its induced ordering.
摘要:本文刻画了(1)导致一类实验完全有序的函数的性质和(2)保持函数Y的诱导有序的变换的性质。
{"title":"Some Properties of Bayesian Orderings of Experiments","authors":"D. Feldman","doi":"10.1214/AOMS/1177692375","DOIUrl":"https://doi.org/10.1214/AOMS/1177692375","url":null,"abstract":"Abstract : The paper characterizes (1) the class of functions which lead to a total ordering of a class of experiments and (2) the class of transformations of a function Y which preserve its induced ordering.","PeriodicalId":50764,"journal":{"name":"Annals of Mathematical Statistics","volume":"100 1","pages":"1428-1440"},"PeriodicalIF":0.0,"publicationDate":"1972-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75657756","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}
The concepts of balance for ordered and for unordered pairs of treatments are introduced. Methods for constructing multistage experimental designs which are Youden designs at each stage, are given. In the construction of these designs an attempt was made to accommodate as much orthogonality and balance (both in our sense and in the classical sense) as is possible. These constructions are presented in several theorems. In one theorem, we give a uniform method of converting $t$ mutually orthogonal Latin squares of order $n$ into a $t$-stage balanced $(n - 1) times n$ Youden designs. Since the known methods of constructing orthogonal Latin squares of order $n = 4t + 2$, for $t > 1$, are not uniform, a uniform method for constructing two-stage $(n - 1) times n$ Youden designs for all even $n$ has been developed. In another theorem, a method of constructing $(2lambda + 1)$-stage balanced $(2lambda + 1) times (4lambda + 3)$ Youden designs, for $4lambda + 3$ a prime power, is presented. A method of constructing $(p^alpha - 1)$-stage balanced $(nu - 1)/2 times nu$ Youden designs is given in another theorem for the case when $v = 4lambda + 3$ and is the product of twin primes, i.e., $nu = p^alpha q^beta, q^beta = p^alpha + 2$. Difference sets based on the elements of Galois fields were utilized for these constructions. Other miscellaneous results are given.
{"title":"Some Families of Designs for Multistage Experiments: Mutually Balanced Youden Designs when the Number of Treatments is Prime Power or Twin Primes. I","authors":"A. Hedayat, E. Seiden, W. Federer","doi":"10.1214/AOMS/1177692384","DOIUrl":"https://doi.org/10.1214/AOMS/1177692384","url":null,"abstract":"The concepts of balance for ordered and for unordered pairs of treatments are introduced. Methods for constructing multistage experimental designs which are Youden designs at each stage, are given. In the construction of these designs an attempt was made to accommodate as much orthogonality and balance (both in our sense and in the classical sense) as is possible. These constructions are presented in several theorems. In one theorem, we give a uniform method of converting $t$ mutually orthogonal Latin squares of order $n$ into a $t$-stage balanced $(n - 1) times n$ Youden designs. Since the known methods of constructing orthogonal Latin squares of order $n = 4t + 2$, for $t > 1$, are not uniform, a uniform method for constructing two-stage $(n - 1) times n$ Youden designs for all even $n$ has been developed. In another theorem, a method of constructing $(2lambda + 1)$-stage balanced $(2lambda + 1) times (4lambda + 3)$ Youden designs, for $4lambda + 3$ a prime power, is presented. A method of constructing $(p^alpha - 1)$-stage balanced $(nu - 1)/2 times nu$ Youden designs is given in another theorem for the case when $v = 4lambda + 3$ and is the product of twin primes, i.e., $nu = p^alpha q^beta, q^beta = p^alpha + 2$. Difference sets based on the elements of Galois fields were utilized for these constructions. Other miscellaneous results are given.","PeriodicalId":50764,"journal":{"name":"Annals of Mathematical Statistics","volume":"63 1","pages":"1517-1527"},"PeriodicalIF":0.0,"publicationDate":"1972-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91116670","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":"Sharp Bounds for the Total Variance of Uniformly Bounded Semimartingales","authors":"L. Dubins","doi":"10.1214/AOMS/1177692388","DOIUrl":"https://doi.org/10.1214/AOMS/1177692388","url":null,"abstract":"","PeriodicalId":50764,"journal":{"name":"Annals of Mathematical Statistics","volume":"50 Pt 6 1","pages":"1559-1565"},"PeriodicalIF":0.0,"publicationDate":"1972-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83891152","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":"Convergence in Distribution of Random Measures","authors":"Miloslav Jiřina","doi":"10.1214/AOMS/1177692410","DOIUrl":"https://doi.org/10.1214/AOMS/1177692410","url":null,"abstract":"","PeriodicalId":50764,"journal":{"name":"Annals of Mathematical Statistics","volume":"42 1","pages":"1727-1731"},"PeriodicalIF":0.0,"publicationDate":"1972-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86782876","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 Limiting Distributions of a Random Number of Dependent Random Variables","authors":"D. L. Thomas","doi":"10.1214/AOMS/1177692409","DOIUrl":"https://doi.org/10.1214/AOMS/1177692409","url":null,"abstract":"","PeriodicalId":50764,"journal":{"name":"Annals of Mathematical Statistics","volume":"24 1","pages":"1719-1726"},"PeriodicalIF":0.0,"publicationDate":"1972-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82819957","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 Structure of the Optimal Stopping Rule in the $S_n/n$ Problem","authors":"M. Thompson, W. L. Owen","doi":"10.1214/AOMS/1177692464","DOIUrl":"https://doi.org/10.1214/AOMS/1177692464","url":null,"abstract":"","PeriodicalId":50764,"journal":{"name":"Annals of Mathematical Statistics","volume":"132 1","pages":"1110-1121"},"PeriodicalIF":0.0,"publicationDate":"1972-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73830250","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":"Maximum and High Level Excursion of a Gaussian Process with Stationary Increments","authors":"S. Berman","doi":"10.1214/AOMS/1177692476","DOIUrl":"https://doi.org/10.1214/AOMS/1177692476","url":null,"abstract":"","PeriodicalId":50764,"journal":{"name":"Annals of Mathematical Statistics","volume":"31 1","pages":"1247-1266"},"PeriodicalIF":0.0,"publicationDate":"1972-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76608806","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}
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