The purpose of this paper is to solve a silent-noisy duel with arbitrary accuracy functions in which both duelists have an imperfect knowledge about the existence of the shot fitted to their gun . As a special case, the solution with only one shot and arbitrary accuracy function for each duelist will be shown.
{"title":"SILENT-NOISY DUEL WITH UNCERTAIN EXISTENCE OF THE SHOT","authors":"Y. Teraoka","doi":"10.5109/13147","DOIUrl":"https://doi.org/10.5109/13147","url":null,"abstract":"The purpose of this paper is to solve a silent-noisy duel with arbitrary accuracy functions in which both duelists have an imperfect knowledge about the existence of the shot fitted to their gun . As a special case, the solution with only one shot and arbitrary accuracy function for each duelist will be shown.","PeriodicalId":287765,"journal":{"name":"Bulletin of Mathematical Statistics","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1981-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117310272","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}
One-way sequential search systems based on pattern matching machines are described. The powers of the systems are evaluated from a viewpoint of formal language theory. Their applicability to medical information processing is briefly discussed.
{"title":"ONE-WAY SEQUENTIAL SEARCH SYSTEMS AND THEIR POWERS","authors":"S. Arikawa","doi":"10.5109/13149","DOIUrl":"https://doi.org/10.5109/13149","url":null,"abstract":"One-way sequential search systems based on pattern matching machines are described. The powers of the systems are evaluated from a viewpoint of formal language theory. Their applicability to medical information processing is briefly discussed.","PeriodicalId":287765,"journal":{"name":"Bulletin of Mathematical Statistics","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1981-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134490581","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 present paper is concerned with the derivation of approxi mate formulae for power components of a sometimes pool test pro cedure applied to a mixed model experiment. A comparison of the values of power components evaluated by these formulae with those calculated using series formulae has been made. I. Introduction. In making inferences from the experimental design models, at times there may arise some doubt regarding the inclusion or not of some of the parameters in the model. For example, in a factorial experiment or an experiment with crossed classi fication the experimenter may be uncertain as to whether interaction parameter(s) should appear in the model. This uncertainty in the model specification may be due to the lack of knowledge, either theoretical or from past experience, in regard to the interaction effect(s) at issue. Such situations of uncertainty lead to conditional speci fication of the model and are to be resolved first before making final inferences. The present study has been made for a mixed model split-plot in time experiment involving conditional specification. We are here mainly interested in making inferences regarding the split-plot treatments (split by time). The uncertainty concerning the inclusion or not of the interactions in this model has been resolved by preliminary tests of significance. 1.1. Related Papers and Objective of the Study. Bozivich, Bancroft and Hartley (1956) have derived approximate formulae and exact formulae for power components of a test procedure in a component of variance model. Derivation of approximate formulae for power in a mixed model has been given by
{"title":"ON CERTAIN APPROXIMATIONS OF POWER OF A TEST PROCEDURE USING TWO PRELIMINARY TESTS IN A MIXED MODEL","authors":"M. A. Ali, S. R. Srivastava","doi":"10.5109/13151","DOIUrl":"https://doi.org/10.5109/13151","url":null,"abstract":"The present paper is concerned with the derivation of approxi mate formulae for power components of a sometimes pool test pro cedure applied to a mixed model experiment. A comparison of the values of power components evaluated by these formulae with those calculated using series formulae has been made. I. Introduction. In making inferences from the experimental design models, at times there may arise some doubt regarding the inclusion or not of some of the parameters in the model. For example, in a factorial experiment or an experiment with crossed classi fication the experimenter may be uncertain as to whether interaction parameter(s) should appear in the model. This uncertainty in the model specification may be due to the lack of knowledge, either theoretical or from past experience, in regard to the interaction effect(s) at issue. Such situations of uncertainty lead to conditional speci fication of the model and are to be resolved first before making final inferences. The present study has been made for a mixed model split-plot in time experiment involving conditional specification. We are here mainly interested in making inferences regarding the split-plot treatments (split by time). The uncertainty concerning the inclusion or not of the interactions in this model has been resolved by preliminary tests of significance. 1.1. Related Papers and Objective of the Study. Bozivich, Bancroft and Hartley (1956) have derived approximate formulae and exact formulae for power components of a test procedure in a component of variance model. Derivation of approximate formulae for power in a mixed model has been given by","PeriodicalId":287765,"journal":{"name":"Bulletin of Mathematical Statistics","volume":"115 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1981-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117336557","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}
Rank statistics to test the null hypothesis that X and Y are conditionally, given Z, independent are given and their asymptotic properties are investigated under the model (X, Y, Z) = (U+ anW, V-FbnW,W) where (U, V) and W are independent. It is shown that linear rank tests given by (X, Y) based on the random sample of size n are asymptotically distribution-free when (an,bn)=n-'12(a,b). It is also shown that Spearman's coefficient of rank correlation and Kendall's coefficient of rank correlation given by (X—czZ, Y—oZ) are asymptotically distribution-free when (an,bn)=(a,b) where (a,b)is some consistent estimator of (a,b).
{"title":"RANK TESTS OF PARTIAL CORRELATION","authors":"S. Shirahata","doi":"10.5109/13144","DOIUrl":"https://doi.org/10.5109/13144","url":null,"abstract":"Rank statistics to test the null hypothesis that X and Y are conditionally, given Z, independent are given and their asymptotic properties are investigated under the model (X, Y, Z) = (U+ anW, V-FbnW,W) where (U, V) and W are independent. It is shown that linear rank tests given by (X, Y) based on the random sample of size n are asymptotically distribution-free when (an,bn)=n-'12(a,b). It is also shown that Spearman's coefficient of rank correlation and Kendall's coefficient of rank correlation given by (X—czZ, Y—oZ) are asymptotically distribution-free when (an,bn)=(a,b) where (a,b)is some consistent estimator of (a,b).","PeriodicalId":287765,"journal":{"name":"Bulletin of Mathematical Statistics","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1981-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128798441","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":"STOPPING RULES FOR SEQUENTIAL DENSITY ESTIMATION","authors":"E. Isogai, 磯貝 英一","doi":"10.5109/13148","DOIUrl":"https://doi.org/10.5109/13148","url":null,"abstract":"","PeriodicalId":287765,"journal":{"name":"Bulletin of Mathematical Statistics","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1981-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131668814","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}
In the previous paper ([5]), we studied the ordinary multiobjective convex program on a locally convex linear topological space in the case that the objective functions and the constraint functions were continuous and convex, but not always Gateaux differ entiable. In the case, we showed that the generalized Kuhn-Tucker conditions given by a subdifferential formula were necessary and sufficient for weak Pareto optimum. In this paper, we consider the ordinary multiobjective program on a Banach space in the case that objective functions and constraint functions are locally Lipschitzian but not always convex, and derive Kuhn-Tucker forms given by Clarke's generalized gradients ([1]) as necessary conditions for weak Pareto optimum. Theorem 2.1 is a generalization of Theorem 1.1 of Schechter ([6]) which is concerned to ordinary pro gram with a scalar-valued objective function. In this paper, X and X* are a real Banach space and its continuous dual, whose origins are denoted by 0 and 0*, respectively. By 0 we denote the empty set.
{"title":"WEAK PARETO OPTIMALITY OF MULTIOBJECTIVE PROBLEM IN A BANACH SPACE","authors":"M. Minami","doi":"10.5109/13145","DOIUrl":"https://doi.org/10.5109/13145","url":null,"abstract":"In the previous paper ([5]), we studied the ordinary multiobjective convex program on a locally convex linear topological space in the case that the objective functions and the constraint functions were continuous and convex, but not always Gateaux differ entiable. In the case, we showed that the generalized Kuhn-Tucker conditions given by a subdifferential formula were necessary and sufficient for weak Pareto optimum. In this paper, we consider the ordinary multiobjective program on a Banach space in the case that objective functions and constraint functions are locally Lipschitzian but not always convex, and derive Kuhn-Tucker forms given by Clarke's generalized gradients ([1]) as necessary conditions for weak Pareto optimum. Theorem 2.1 is a generalization of Theorem 1.1 of Schechter ([6]) which is concerned to ordinary pro gram with a scalar-valued objective function. In this paper, X and X* are a real Banach space and its continuous dual, whose origins are denoted by 0 and 0*, respectively. By 0 we denote the empty set.","PeriodicalId":287765,"journal":{"name":"Bulletin of Mathematical Statistics","volume":"98 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1981-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128715107","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 NORMALITY OF RANK SUMS UNDER DEPENDENCY AND ITS APPLICATIONS TO THE TESTING PROBLEM","authors":"Ryoji Tamura","doi":"10.5109/13143","DOIUrl":"https://doi.org/10.5109/13143","url":null,"abstract":"","PeriodicalId":287765,"journal":{"name":"Bulletin of Mathematical Statistics","volume":"83 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1981-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131749888","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 STOCHASTIC APPROXIMATION WITH A SEQUENCE OF DEPENDENT RANDOM VARIABLES","authors":"Masafumi Watanabe","doi":"10.5109/13146","DOIUrl":"https://doi.org/10.5109/13146","url":null,"abstract":"","PeriodicalId":287765,"journal":{"name":"Bulletin of Mathematical Statistics","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1981-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116286030","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}
We define non-cooperative game systems and cooperative game systems from a viewpoint of information theory. Concerning the both systems we show some sufficient conditions under which players can obtain the total information on the other players' strategies from a sequence of observations. In a cooperative case we give a numerical model and calculate the amounts of information obtained from the sequential observations by the players in a cooperative group.
{"title":"AN INFORMATION THEORY OF GAME SYSTEMS","authors":"Yuichi Kai, Seigo Kanô","doi":"10.5109/13150","DOIUrl":"https://doi.org/10.5109/13150","url":null,"abstract":"We define non-cooperative game systems and cooperative game systems from a viewpoint of information theory. Concerning the both systems we show some sufficient conditions under which players can obtain the total information on the other players' strategies from a sequence of observations. In a cooperative case we give a numerical model and calculate the amounts of information obtained from the sequential observations by the players in a cooperative group.","PeriodicalId":287765,"journal":{"name":"Bulletin of Mathematical Statistics","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1981-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132431280","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 SEQUENTIAL SELECTION PLAN WITH PALY-THE-WINNER SAMPLING AND SUCCESSIVE SUCCESS STOPPING RULE IN A FINITE POPULATION","authors":"K. Jojima, C. Asano","doi":"10.5109/13141","DOIUrl":"https://doi.org/10.5109/13141","url":null,"abstract":"","PeriodicalId":287765,"journal":{"name":"Bulletin of Mathematical Statistics","volume":"14 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":"132776544","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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