An important problem in spatial statistics is to predict the unobserved value z(s0) at a specified location so based on the information of n observations z(sƒ¿), α = 1, ¥¥¥, n. It can be achieved in three stages of (1) estimating the variograms, (2) fitting a model to the estimated variograms, and (3) applying the so-called ordinary (or universal) kriging. The present article proposes a method to detect influential observations in variogram estimation, variogram model fitting to the estimated variograms, and spatial prediction using the fitted variogram model. To do this, we derive the influence functions for statistics in the above three stages assuming that the underlying process of the observed spatial data is second-order stationary. A real numerical example is analyzed to show the validity or usefulness of the proposed influence functions. Comparison is made with the influence function derived by Gunst and Hartfield (1997).
{"title":"SENSITIVITY ANALYSIS IN SPATIAL STATISTICS : DETECTING INFLUENTIAL OBSERVATIONS IN SPATIAL PREDICTION","authors":"Seung-Bae Choi, Y. Tanaka","doi":"10.5183/JJSCS1988.13.25","DOIUrl":"https://doi.org/10.5183/JJSCS1988.13.25","url":null,"abstract":"An important problem in spatial statistics is to predict the unobserved value z(s0) at a specified location so based on the information of n observations z(sƒ¿), α = 1, ¥¥¥, n. It can be achieved in three stages of (1) estimating the variograms, (2) fitting a model to the estimated variograms, and (3) applying the so-called ordinary (or universal) kriging. The present article proposes a method to detect influential observations in variogram estimation, variogram model fitting to the estimated variograms, and spatial prediction using the fitted variogram model. To do this, we derive the influence functions for statistics in the above three stages assuming that the underlying process of the observed spatial data is second-order stationary. A real numerical example is analyzed to show the validity or usefulness of the proposed influence functions. Comparison is made with the influence function derived by Gunst and Hartfield (1997).","PeriodicalId":338719,"journal":{"name":"Journal of the Japanese Society of Computational Statistics","volume":"76 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124839081","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 are going to compare the exact unconditional powers resulting from using three well known goodness-of-fit statistics, i.e., Pearson's X2, deviance and power divergence, in testing conditionally and exactly the equality of three binomial proportions. As far as I know, no paper has paid any attention to the selection of test statistics in the context of an exact conditional test. This is partly because almost all authors, apart from Mehta and Hilton (1993), have treated two binomial proportions, where signed root of each frequently used goodness-of-fit statistic is a monotonous function of an observed value on a conditional reference set. Theoretical investigations are carried out and numerical results are obtained on various settings of binomial parameters.
{"title":"EXACT UNCONDITIONAL POWER COMPARISON OF THREE STATISTICS IN TESTING THE EQUALITY OF THREE BINOMIAL PROPORTIONS","authors":"Akihiko Matsuo","doi":"10.5183/JJSCS1988.12.1","DOIUrl":"https://doi.org/10.5183/JJSCS1988.12.1","url":null,"abstract":"We are going to compare the exact unconditional powers resulting from using three well known goodness-of-fit statistics, i.e., Pearson's X2, deviance and power divergence, in testing conditionally and exactly the equality of three binomial proportions. As far as I know, no paper has paid any attention to the selection of test statistics in the context of an exact conditional test. This is partly because almost all authors, apart from Mehta and Hilton (1993), have treated two binomial proportions, where signed root of each frequently used goodness-of-fit statistic is a monotonous function of an observed value on a conditional reference set. Theoretical investigations are carried out and numerical results are obtained on various settings of binomial parameters.","PeriodicalId":338719,"journal":{"name":"Journal of the Japanese Society of Computational Statistics","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116625160","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":"Two estimated snow load curves and the bootstrap significance test","authors":"H. Sakurai, M. Taguri, Masaki Ishiduka","doi":"10.5183/JJSCS1988.12.51","DOIUrl":"https://doi.org/10.5183/JJSCS1988.12.51","url":null,"abstract":"","PeriodicalId":338719,"journal":{"name":"Journal of the Japanese Society of Computational Statistics","volume":"78 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124108303","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":"SELECTION AND ORDERING OF VARIABLES IN DISCRIMINANT ANALYSIS AND APPLICATION TO BEHRENS-FISHER MODEL","authors":"T. Yamashita","doi":"10.5183/JJSCS1988.12.15","DOIUrl":"https://doi.org/10.5183/JJSCS1988.12.15","url":null,"abstract":"","PeriodicalId":338719,"journal":{"name":"Journal of the Japanese Society of Computational Statistics","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117036145","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 probability-updating method in probabilistic expert systems is considered in this paper based on the minimum discrimination information. Here, newly acquired information is taken as the latest true marginal probabilities, not as newly observed data with the same weight as previous data. Posterior probabilities are obtained by updating prior probabilities subject to the latest true marginals. To apply to probabilistic expert systems, we extend Ku and Kullback(1968)’s the minimum discrimination information method for saturated models to log-linear models, discuss localization of global updating, and show that Deming and Stephan’s iterative procedure can also be used to find the posterior probabilities. Our updating method can also be used to handle uncertain evidences in probabilistic expert systems.
{"title":"MINIMUM INFORMATION UPDATING WITH SPECIFIED MARGINALS IN PROBABILISTIC EXPERT SYSTEMS","authors":"M. Kuroda, Z. Geng","doi":"10.5183/JJSCS1988.12.41","DOIUrl":"https://doi.org/10.5183/JJSCS1988.12.41","url":null,"abstract":"A probability-updating method in probabilistic expert systems is considered in this paper based on the minimum discrimination information. Here, newly acquired information is taken as the latest true marginal probabilities, not as newly observed data with the same weight as previous data. Posterior probabilities are obtained by updating prior probabilities subject to the latest true marginals. To apply to probabilistic expert systems, we extend Ku and Kullback(1968)’s the minimum discrimination information method for saturated models to log-linear models, discuss localization of global updating, and show that Deming and Stephan’s iterative procedure can also be used to find the posterior probabilities. Our updating method can also be used to handle uncertain evidences in probabilistic expert systems.","PeriodicalId":338719,"journal":{"name":"Journal of the Japanese Society of Computational Statistics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116308257","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}
Y. Yoshizawa, Hiroshi Kimura, H. Inoue, Keiko Fujita, M. Toyama, O. Miyatake
We have developed a physical random number generator in which radioactivity, i.e., one of the most random phenomena, is used. The long-lived radioactive nuclide 241 Am and a clock pulse generator are used for generating random pulses and regular pulses, respectively. A 1024 channel scaler counts clock pulses between two consecutive random pulses. This procedure is repeated and the counts are stored in a computer. The last digit of a count at the scaler gives a digit of uniform physical random number. We have tested our random numbers for randomness and uniformity, and stored 600 million random digits on each compact disc for users.
{"title":"PHYSICAL RANDOM NUMBERS GENERATED BY RADIOACTIVITY","authors":"Y. Yoshizawa, Hiroshi Kimura, H. Inoue, Keiko Fujita, M. Toyama, O. Miyatake","doi":"10.5183/JJSCS1988.12.67","DOIUrl":"https://doi.org/10.5183/JJSCS1988.12.67","url":null,"abstract":"We have developed a physical random number generator in which radioactivity, i.e., one of the most random phenomena, is used. The long-lived radioactive nuclide 241 Am and a clock pulse generator are used for generating random pulses and regular pulses, respectively. A 1024 channel scaler counts clock pulses between two consecutive random pulses. This procedure is repeated and the counts are stored in a computer. The last digit of a count at the scaler gives a digit of uniform physical random number. We have tested our random numbers for randomness and uniformity, and stored 600 million random digits on each compact disc for users.","PeriodicalId":338719,"journal":{"name":"Journal of the Japanese Society of Computational Statistics","volume":"238 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114475112","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":"TWO-STAGE TESTING TO ESTABLISH NON-INFERIORITY IN THE STRATIFIED 2×2 CONTINGENCY TABLES","authors":"T. Koshimizu, M. Tsujitani","doi":"10.5183/JJSCS1988.11.25","DOIUrl":"https://doi.org/10.5183/JJSCS1988.11.25","url":null,"abstract":"","PeriodicalId":338719,"journal":{"name":"Journal of the Japanese Society of Computational Statistics","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1998-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123964806","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 NUMERICAL COMPUTATION OF CONFLUENT HYPERGEOMETRIC FUNCTION WITH ZONAL POLYNOMIALS OF ORDER 3","authors":"T. Sugiyama, Y. Takeda, Masafumi Fukuda","doi":"10.5183/JJSCS1988.11.1","DOIUrl":"https://doi.org/10.5183/JJSCS1988.11.1","url":null,"abstract":"","PeriodicalId":338719,"journal":{"name":"Journal of the Japanese Society of Computational Statistics","volume":"73 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1998-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115932612","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 study is concerned with estimating the bivariate normal mean vector (ƒÊ = (ƒÊi ƒÊ2)•Œ) for the case where one has a prior information about the mean vector in the form of preliminary conjectured intervals, ƒÊi • ̧ [ƒÉi ƒÂi, ƒÉi + ƒÂi], for ƒÂi > 0, i = 1, 2. It is based on the minimum discrimination information(MDI) approach, intended to propose and develop an estimator that has lower risk than a usual estimator (m.l.e.) in or beyond the conjectured intervals. The MDI estimator is obtained for the constrained estimation. This yields a shrinkage type estimator that shrinks towards the preliminary conjectured intervals. Its risk is evaluated and compared with the usual estimator under a quadratic loss function. Favorable properties of the proposed estimator are noted and recommendations for its use are also made.
{"title":"A SHRINKAGE ESTIMATOR OF THE BIVARIATE NORMAL MEAN WITH INTERVAL RESTRICTIONS","authors":"Hea-Jung Kim, Kōichi Inada, Hiroshi Yadohisa","doi":"10.5183/JJSCS1988.11.79","DOIUrl":"https://doi.org/10.5183/JJSCS1988.11.79","url":null,"abstract":"This study is concerned with estimating the bivariate normal mean vector (ƒÊ = (ƒÊi ƒÊ2)•Œ) for the case where one has a prior information about the mean vector in the form of preliminary conjectured intervals, ƒÊi • ̧ [ƒÉi ƒÂi, ƒÉi + ƒÂi], for ƒÂi > 0, i = 1, 2. It is based on the minimum discrimination information(MDI) approach, intended to propose and develop an estimator that has lower risk than a usual estimator (m.l.e.) in or beyond the conjectured intervals. The MDI estimator is obtained for the constrained estimation. This yields a shrinkage type estimator that shrinks towards the preliminary conjectured intervals. Its risk is evaluated and compared with the usual estimator under a quadratic loss function. Favorable properties of the proposed estimator are noted and recommendations for its use are also made.","PeriodicalId":338719,"journal":{"name":"Journal of the Japanese Society of Computational Statistics","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1998-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129909887","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 POWER APPROXIMATION OF THE TEST OF INDEPENDENCE IN s×r CONTINGENCY TABLES BASED ON A NORMALIZING TRANSFORMATION","authors":"Y. Sekiya, N. Taneichi, H. Imai","doi":"10.5183/JJSCS1988.11.65","DOIUrl":"https://doi.org/10.5183/JJSCS1988.11.65","url":null,"abstract":"","PeriodicalId":338719,"journal":{"name":"Journal of the Japanese Society of Computational Statistics","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1998-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117237592","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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