{"title":"Monotone Median Regression","authors":"J. Cryer, Tim Robertson, F. T. Wright, R. Casady","doi":"10.1214/AOMS/1177692378","DOIUrl":"https://doi.org/10.1214/AOMS/1177692378","url":null,"abstract":"","PeriodicalId":50764,"journal":{"name":"Annals of Mathematical Statistics","volume":"36 1","pages":"1459-1469"},"PeriodicalIF":0.0,"publicationDate":"1972-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85772749","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 Asymptotic Noncentral Distribution of Hotelling's Generalized $T_0^2$","authors":"R. Muirhead","doi":"10.1214/AOMS/1177692400","DOIUrl":"https://doi.org/10.1214/AOMS/1177692400","url":null,"abstract":"","PeriodicalId":50764,"journal":{"name":"Annals of Mathematical Statistics","volume":"8 1","pages":"1671-1677"},"PeriodicalIF":0.0,"publicationDate":"1972-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82701095","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 TWO RECENT PAPERS ON ERGODICITY IN NONHOMOGENEOUS MARKOV CHAINS","authors":"M. Iosifescu","doi":"10.1214/AOMS/1177692411","DOIUrl":"https://doi.org/10.1214/AOMS/1177692411","url":null,"abstract":"","PeriodicalId":50764,"journal":{"name":"Annals of Mathematical Statistics","volume":"15 1","pages":"1732-1736"},"PeriodicalIF":0.0,"publicationDate":"1972-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83648982","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}
On the marginal distributions of the latent roots of the multivariate beta matrix The marginal distributions of the latent roots of the multivariate beta matrix are shown to constitute a complete system of solutions of an ordinary differential equation (d.e.), which is related to the author's d.e. 's for Rotelling's generalized T 2 and Pillai's V(m) statistics. Similar results are o given for the latent roots of the multivariate F and Wishart matrices (E=I). Pillai's approximations to the distributions of the largest and smallest roots are interpreted as exact solutions, the contributions of higher order solutions being neglected. m ~(q-m-l) m ~(n-m-l) The marginal distributions of the individual £, have been investigated by ~ (1) (2) On the marginal distributions of the latent roots of the multivariate beta mattix* q,n ~ m. The latent roots £1 > • • • > £m > 0 of the multivariate beta matrix B = S(S+T)-l are well known to have the joint density function
{"title":"On the Marginal Distributions of the Latent Roots of the Multivariate Beta Matrix","authors":"A. W. Davis","doi":"10.1214/AOMS/1177692399","DOIUrl":"https://doi.org/10.1214/AOMS/1177692399","url":null,"abstract":"On the marginal distributions of the latent roots of the multivariate beta matrix The marginal distributions of the latent roots of the multivariate beta matrix are shown to constitute a complete system of solutions of an ordinary differential equation (d.e.), which is related to the author's d.e. 's for Rotelling's generalized T 2 and Pillai's V(m) statistics. Similar results are o given for the latent roots of the multivariate F and Wishart matrices (E=I). Pillai's approximations to the distributions of the largest and smallest roots are interpreted as exact solutions, the contributions of higher order solutions being neglected. m ~(q-m-l) m ~(n-m-l) The marginal distributions of the individual £, have been investigated by ~ (1) (2) On the marginal distributions of the latent roots of the multivariate beta mattix* q,n ~ m. The latent roots £1 > • • • > £m > 0 of the multivariate beta matrix B = S(S+T)-l are well known to have the joint density function","PeriodicalId":50764,"journal":{"name":"Annals of Mathematical Statistics","volume":"23 1","pages":"1664-1670"},"PeriodicalIF":0.0,"publicationDate":"1972-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74610317","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":"Correction Notes: Correction to \"Multivariate Procedures Invariant Under Linear Transformations\"","authors":"R. Obenchain","doi":"10.1214/AOMS/1177692414","DOIUrl":"https://doi.org/10.1214/AOMS/1177692414","url":null,"abstract":"","PeriodicalId":50764,"journal":{"name":"Annals of Mathematical Statistics","volume":"19 1","pages":"1742-1743"},"PeriodicalIF":0.0,"publicationDate":"1972-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86026844","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":"Completeness for a Family of Multivariate Normal Distributions","authors":"J. Seely","doi":"10.1214/AOMS/1177692396","DOIUrl":"https://doi.org/10.1214/AOMS/1177692396","url":null,"abstract":"","PeriodicalId":50764,"journal":{"name":"Annals of Mathematical Statistics","volume":"61 1","pages":"1644-1647"},"PeriodicalIF":0.0,"publicationDate":"1972-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84693553","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 the Test of Independence Between Two Sets of Variates","authors":"R. Muirhead","doi":"10.1214/AOMS/1177692381","DOIUrl":"https://doi.org/10.1214/AOMS/1177692381","url":null,"abstract":"","PeriodicalId":50764,"journal":{"name":"Annals of Mathematical Statistics","volume":"19 1","pages":"1491-1497"},"PeriodicalIF":0.0,"publicationDate":"1972-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85762334","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":"Stochastic Order Relationships Between GI/G/k Systems","authors":"D. R. Jacobs, S. Schach","doi":"10.1214/AOMS/1177692394","DOIUrl":"https://doi.org/10.1214/AOMS/1177692394","url":null,"abstract":"","PeriodicalId":50764,"journal":{"name":"Annals of Mathematical Statistics","volume":"5 1","pages":"1623-1633"},"PeriodicalIF":0.0,"publicationDate":"1972-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89252294","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 of Quantile and Spacings Processes with Applications","authors":"G. Shorack","doi":"10.1214/AOMS/1177692373","DOIUrl":"https://doi.org/10.1214/AOMS/1177692373","url":null,"abstract":"","PeriodicalId":50764,"journal":{"name":"Annals of Mathematical Statistics","volume":"21 1","pages":"1400-1411"},"PeriodicalIF":0.0,"publicationDate":"1972-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79203148","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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