15292

1490 دكتري

دكتري

آمار (طرح و تجزيه آزمايش ها)

اصفهان : دانشگاه صنعتي اصفهان

1398

چهار، 73ص: جدول

سعيد پولادساز

كاتارژينا فيليپياك

هوشنگ طالبي، بهناز عمومي، ايرج كاظمي

1398/08/22

كتابنامه

رياضي

رياضي

1398/09/02

2577482

Optimal block designs under some correlation structures Razieh Khodsiani razieh khodsiani@math iut ac ir September 18 2019 Ph D of Science Thesis in Farsi Departement of Mathematical Sciences Isfahan University of Technology Isfahan 84156 8311 IranSupervisor Dr Saeid Pooladsaz spooladsaz@cc iut ac irAdvisor Dr Katarczyna Filipiak katarczyna filipiak@put poznan pl2010 MSC 62K05 62K10Keywords Block design Circular block design Hub correlation Circular autoregression of order one Universallyoptimal design E optimal design Abstract This PhD thesis is based on the following papers S Universal optimal block designs under hub correlation structure Statistics K R P and Probability Letters 129 2017 387 392 A Optimality of block designs under circular autoregressive cor F K K R M relation of order one Statistical Papers 60 2019 77 97 S Optimality of balanced block designs for correlated observations Canadian K R P journal of statistics 2019 submittedThe block experiments have been widely used in sciences medical and engineering Universal optimal block designsunder general correlation structures are usually difficult to specify theoretically or algorithmically However theycan sometimes be found for a specific correlation with particular parameter values There are different correlationstructures for the observations which are considered by many researchers Hub correlation structure has widely application in some network and other similar experiments see Zhu and Coster 43 According to the correlation values there are some different cases for this correlation structure In this Thesis we consider two different cases of hub correlation structure and we present a method to construct the universallyoptimal block designs without using the semibalanced array SBA method Circular autoregression AR 1 C is an autoregression correlation structure for circular block designs We alsopresent the universal optimality of some circular nondirectionally neighbor balanced designs under AR 1 C forany values of correlation coefficient Existence of universally optimal designs often has some limitations and for some combinations of design parametersthe universally optimal designs may not exist In such a case efficiency of some designs or optimality with respect tothe specified criteria is considered In UPOV The International Union for the Protection of New Varieties of Plants research complete block designs are recommended in experiments when the number of treatments is less than 16 The designs with the same number of blocks as number of treatments and units are also applied in clinical trials Inthis Thesis some E optimal complete circular block designs are characterized IntroductionLet the class of block designs is considered as v b k where v b and k are respectively the number of treatments blocks and plots per block We assume that observations in different blocks are uncorrelated but that observationswithin blocks are correlated with the same correlation structure in each block A standard model associated with ablock design d can be written as 31 y Xd B

سعيد پولادساز

كاتارژينا فيليپياك

هوشنگ طالبي، بهناز عمومي، ايرج كاظمي