{"title":"ON EFFICIENCY OF INFERENCES OF TRANSITION PROBABILITIES TO MARKOVIAN DECISION PROCESSES","authors":"Kingo Kobayashi, H. Fujikawa, M. Kurano","doi":"10.5109/13077","DOIUrl":"https://doi.org/10.5109/13077","url":null,"abstract":"","PeriodicalId":287765,"journal":{"name":"Bulletin of Mathematical Statistics","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1973-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131677448","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 OF A SEQUENTIAL ESTIMATOR OF A PROBABILITY DENSITY FUNCTION","authors":"H. Davies","doi":"10.5109/13071","DOIUrl":"https://doi.org/10.5109/13071","url":null,"abstract":"","PeriodicalId":287765,"journal":{"name":"Bulletin of Mathematical Statistics","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1973-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125888615","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}
where for at last one is (s= 1, ••• , r), the strict inequality Ois > eis+, holds in Hil-irO• Let D. be the decision to accept the corresponding hypothesis H., Pr {D.IH'.} be the probability of making decision D. when fr. is true, and Pr {D. I H"} be the conditional probability of making decision D., given the decision D'. when is true. Under the situation that we can be sure of the existence of the true hypothesis
其中对于最后一个是(s= 1，•••••，r)，则严格不等式Ois > eis+在hill - iro中成立•设d为接受相应假设H.， Pr {D. ih '的决定。表示当f .为真时做出决策D的概率，Pr {D。I H '}表示在给定决策D'的情况下，做出决策D的条件概率。何时为真。在我们可以确定真假设存在的情况下
{"title":"SUCCESIVE MULTIPLE DECISION PROCEDURES FOR ORDERED PARAMETERS","authors":"M. Tasaka","doi":"10.5109/13068","DOIUrl":"https://doi.org/10.5109/13068","url":null,"abstract":"where for at last one is (s= 1, ••• , r), the strict inequality Ois > eis+, holds in Hil-irO• Let D. be the decision to accept the corresponding hypothesis H., Pr {D.IH'.} be the probability of making decision D. when fr. is true, and Pr {D. I H\"} be the conditional probability of making decision D., given the decision D'. when is true. Under the situation that we can be sure of the existence of the true hypothesis","PeriodicalId":287765,"journal":{"name":"Bulletin of Mathematical Statistics","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1973-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124970691","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 class of estimators of a distribution function, which includes the empirical distribution function, is discussed. The necessary and sufficient condition for the estimator to be asymptotically unbiased at all continuity points of the distribution function is presented. We give the asymptotic evaluation of the variance and show its asymptotic normality. The necessary and sufficient condition for the estimator to converge uniformly to a continuous distribution function with probability one is presented (the continuity can be delected in case of the necessary condition). We propose an estimator of a p-th quantile based on the estimator of a distribution function, which converges to the p-th quantile with probability one under certain conditions.
{"title":"UNIFORM CONVERGENCE OF AN ESTIMATOR OF A DISTRIBUTION FUNCTION","authors":"Hajime Yamato","doi":"10.5109/13073","DOIUrl":"https://doi.org/10.5109/13073","url":null,"abstract":"A class of estimators of a distribution function, which includes the empirical distribution function, is discussed. The necessary and sufficient condition for the estimator to be asymptotically unbiased at all continuity points of the distribution function is presented. We give the asymptotic evaluation of the variance and show its asymptotic normality. The necessary and sufficient condition for the estimator to converge uniformly to a continuous distribution function with probability one is presented (the continuity can be delected in case of the necessary condition). We propose an estimator of a p-th quantile based on the estimator of a distribution function, which converges to the p-th quantile with probability one under certain conditions.","PeriodicalId":287765,"journal":{"name":"Bulletin of Mathematical Statistics","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1973-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123328765","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 GRADIENT METHOD UTILIZING APRIORI STOCHASTIC INFORMATION ABOUT THE LOCATION OF THE MINIMUM","authors":"Kumiko Ito","doi":"10.5109/13076","DOIUrl":"https://doi.org/10.5109/13076","url":null,"abstract":"","PeriodicalId":287765,"journal":{"name":"Bulletin of Mathematical Statistics","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1973-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116789045","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":"SOME STATISTICAL PROPERTIES OF ESTIMATORS OF DENSITY AND DISTRIBUTION FUNCTIONS","authors":"Hajime Yamato, 大和 元","doi":"10.5109/13066","DOIUrl":"https://doi.org/10.5109/13066","url":null,"abstract":"","PeriodicalId":287765,"journal":{"name":"Bulletin of Mathematical Statistics","volume":"70 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1972-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125262742","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":"GENERATIVE AND GENEALOGICAL CLASSIFICATIONS OF ALL THE CONFIGURATIONS IN AN $ M TIMES N $ CELL SPACE UNDER APPLICATIONS LOCAL MAJORITY TRANSFORMATION : INFORMATION SCIENCE APPROACH TO BIOMATHEMATICS, XIII","authors":"T. Kitagawa","doi":"10.5109/13065","DOIUrl":"https://doi.org/10.5109/13065","url":null,"abstract":"","PeriodicalId":287765,"journal":{"name":"Bulletin of Mathematical Statistics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1972-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115996446","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 this paper we shall treat the optimal control problem in continuous time Markov decision processes having a Borel state space and a compact action space varying with both the time and the state. The cost functional we consider here is the sum of the integral over the finite horizon of a return rate which depends on both the controller and the corresponding response, and the expected return of the system at the final fixed time. Our optimal control problem is to find a controller which maximzie the cost functional over the given planning horizon. Main results are a necessary and sufficient condition for an optimality, and an algorithm for finding the optimal controller. B. L. Miller [1] treated the problem similar to ours, but his paper was restricted to the case of the finite state space and action space. Our situation is succeeded owing to the implicit function's lemma of K. Tsuji and N. Furukawa [3]. The method of construction of our algorithm is often used in Dynamic Programming problem, for example in [4].
本文研究连续时间马尔可夫决策过程的最优控制问题，该决策过程具有随时间和状态变化的Borel状态空间和紧致作用空间。我们在这里考虑的代价函数是在有限范围内的收益率积分的和，这取决于控制器和相应的响应，以及系统在最终固定时间的期望收益。我们的最优控制问题是在给定的规划范围内找到一个使成本函数最大的控制器。主要结果是最优性的充分必要条件，以及寻找最优控制器的算法。B. L. Miller[1]处理的问题与我们的类似，但他的论文仅限于有限状态空间和动作空间的情况。由于K. Tsuji和N. Furukawa[3]的隐函数引理，我们的情况得以成功。本文算法的构造方法常用于动态规划问题，如文献[4]。
{"title":"ON THE EXISTENCE OF OPTIMAL CONTROL IN CONTINUOUS TIME MARKOV DECISION PROCESSES","authors":"M. Yasuda","doi":"10.5109/13058","DOIUrl":"https://doi.org/10.5109/13058","url":null,"abstract":"In this paper we shall treat the optimal control problem in continuous time Markov decision processes having a Borel state space and a compact action space varying with both the time and the state. The cost functional we consider here is the sum of the integral over the finite horizon of a return rate which depends on both the controller and the corresponding response, and the expected return of the system at the final fixed time. Our optimal control problem is to find a controller which maximzie the cost functional over the given planning horizon. Main results are a necessary and sufficient condition for an optimality, and an algorithm for finding the optimal controller. B. L. Miller [1] treated the problem similar to ours, but his paper was restricted to the case of the finite state space and action space. Our situation is succeeded owing to the implicit function's lemma of K. Tsuji and N. Furukawa [3]. The method of construction of our algorithm is often used in Dynamic Programming problem, for example in [4].","PeriodicalId":287765,"journal":{"name":"Bulletin of Mathematical Statistics","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1972-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134207955","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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