For the estimable parameter of degree 2, throughout this paper, we consider 02 with h2 such that h2(x, x) and h2(x, x)=0 for any x, yEX. As estimators of estimable parameters, U-statistics and differentiable statistical functions are well known. (See, for example, Hoeffding (1948) and von Mises (1947).) For an estimable parameter of degree 1, the U-statistic is identical with the differ entiable statistical function, which is given by
{"title":"BAYES RISKS OF ESTIMATORS OF ESTIMABLE PARAMETERS","authors":"Hajime Yamato, 大和 元","doi":"10.5109/13136","DOIUrl":"https://doi.org/10.5109/13136","url":null,"abstract":"For the estimable parameter of degree 2, throughout this paper, we consider 02 with h2 such that h2(x, x) and h2(x, x)=0 for any x, yEX. As estimators of estimable parameters, U-statistics and differentiable statistical functions are well known. (See, for example, Hoeffding (1948) and von Mises (1947).) For an estimable parameter of degree 1, the U-statistic is identical with the differ entiable statistical function, which is given by","PeriodicalId":287765,"journal":{"name":"Bulletin of Mathematical Statistics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1980-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129817455","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}
A reversal operation for dynamic programming (DP) trans forms a (main) control process to a reversed control process. It is applied to the well known linear equation and quadratic criterion control process and to a terminal control process. Not solving the recursive equation directly, but merely applying the author's Reverse Theorem in DP, we can automatically obtain the solution of the recursive equation for reversed process.
{"title":"REVERSED CONTROL PROCESSES","authors":"Seiichi Iwamoto","doi":"10.5109/13135","DOIUrl":"https://doi.org/10.5109/13135","url":null,"abstract":"A reversal operation for dynamic programming (DP) trans forms a (main) control process to a reversed control process. It is applied to the well known linear equation and quadratic criterion control process and to a terminal control process. Not solving the recursive equation directly, but merely applying the author's Reverse Theorem in DP, we can automatically obtain the solution of the recursive equation for reversed process.","PeriodicalId":287765,"journal":{"name":"Bulletin of Mathematical Statistics","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1980-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124829397","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 FINITE PARAMETRIC LINEAR MODELS OF DYADIC STATIONARY PROCESSES","authors":"T. Nagai","doi":"10.5109/13139","DOIUrl":"https://doi.org/10.5109/13139","url":null,"abstract":"","PeriodicalId":287765,"journal":{"name":"Bulletin of Mathematical Statistics","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1980-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124890223","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":"NEARLY OPTIMAL POLICIES AND STOPPING TIMES IN MARKOV DECISION PROCESSES WITH GENERAL REWARDS","authors":"N. Furukawa","doi":"10.5109/13142","DOIUrl":"https://doi.org/10.5109/13142","url":null,"abstract":"","PeriodicalId":287765,"journal":{"name":"Bulletin of Mathematical Statistics","volume":"66 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1980-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129024289","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":"STRONG CONSISTENCY AND OPTIMALITY OF A SEQUENTIAL DENSITY ESTIMATOR","authors":"E. Isogai","doi":"10.5109/13140","DOIUrl":"https://doi.org/10.5109/13140","url":null,"abstract":"","PeriodicalId":287765,"journal":{"name":"Bulletin of Mathematical Statistics","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1980-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134544989","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 purpose of this paper is to solve the single-bullet duel in which either silent or noisy is uncertain and the accuracy functions are arbitrary. It will be found the model in this paper is an extension of the single-bullet duels : silent, noisy, and silent-noisy duels.
{"title":"A SINGLE-BULLET DUEL WITH UNCERTAIN INFORMATION AVAILABLE TO THE DUELISTS","authors":"Y. Teraoka","doi":"10.5109/13132","DOIUrl":"https://doi.org/10.5109/13132","url":null,"abstract":"The purpose of this paper is to solve the single-bullet duel in which either silent or noisy is uncertain and the accuracy functions are arbitrary. It will be found the model in this paper is an extension of the single-bullet duels : silent, noisy, and silent-noisy duels.","PeriodicalId":287765,"journal":{"name":"Bulletin of Mathematical Statistics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1979-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130735386","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}
This paper is a continuation of our papers [9], [10] and [11] and is concerned with a Robbins-Monro type stochastic approximation method when a sequence of dependently distributed random vectors is given. The method of stochastic approximation has been first proposed by H. Robbins and S. Monro ([5]) and its modifications have been thereafter given by many authors. A typical one of them is as follows. Suppose that an RN-valued random vector Y„(x) can be observed at xERN and each instant n, and the expected value of Y n(X), denoted by E[Y„(x)]=1/17,(x), is unknown to us. Assuming that the equation itin(x)=0 has a solution x=8,, for each n=1, 2, • , it is desire to estimate 0,, for sufficiently large n on the basis of observed values Y1(X0), Y2(Xi), Y.+I(X,i), ••• at the points X„ Xi, •-• , X„, ••• which are produced by the following recurrence relation,
{"title":"AN ALMOST SURE CONVERGENCE THEOREM IN A STOCHASTIC APPROXIMATION METHOD WITH DEPENDENT RANDOM VARIABLES","authors":"Masafumi Watanabe","doi":"10.5109/13134","DOIUrl":"https://doi.org/10.5109/13134","url":null,"abstract":"This paper is a continuation of our papers [9], [10] and [11] and is concerned with a Robbins-Monro type stochastic approximation method when a sequence of dependently distributed random vectors is given. The method of stochastic approximation has been first proposed by H. Robbins and S. Monro ([5]) and its modifications have been thereafter given by many authors. A typical one of them is as follows. Suppose that an RN-valued random vector Y„(x) can be observed at xERN and each instant n, and the expected value of Y n(X), denoted by E[Y„(x)]=1/17,(x), is unknown to us. Assuming that the equation itin(x)=0 has a solution x=8,, for each n=1, 2, • , it is desire to estimate 0,, for sufficiently large n on the basis of observed values Y1(X0), Y2(Xi), Y.+I(X,i), ••• at the points X„ Xi, •-• , X„, ••• which are produced by the following recurrence relation,","PeriodicalId":287765,"journal":{"name":"Bulletin of Mathematical Statistics","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1979-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133353495","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 METHOD OF H. CHERNOFF IN CLASSIFICATORY PROBLEM BETWEEN TWO CATEGORIES WITH SPECIFIED $ 2^k $-th MOMENT ($ k = 0, 1, 2 $)","authors":"A. Nishi, 西 晃央","doi":"10.5109/13130","DOIUrl":"https://doi.org/10.5109/13130","url":null,"abstract":"","PeriodicalId":287765,"journal":{"name":"Bulletin of Mathematical Statistics","volume":"72 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1979-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130430450","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}
Four new statistics to test the homogeneity of means and of variances against the ordered alternatives are considered and their power properties are investigated with the aid of computer simulations. These statistics are extensions of a partial ordering on the sample space induced by the likelihood ratio. It is found that they are more powerful than the likelihood ratio tests.
{"title":"TESTS OF HOMOGENEITY FOR ORDERED ALTERNATIVES IN THE NORMAL POPULATIONS","authors":"S. Shirahata","doi":"10.5109/13131","DOIUrl":"https://doi.org/10.5109/13131","url":null,"abstract":"Four new statistics to test the homogeneity of means and of variances against the ordered alternatives are considered and their power properties are investigated with the aid of computer simulations. These statistics are extensions of a partial ordering on the sample space induced by the likelihood ratio. It is found that they are more powerful than the likelihood ratio tests.","PeriodicalId":287765,"journal":{"name":"Bulletin of Mathematical Statistics","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1979-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127098533","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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