11597

10646

كارشناسي ارشد

آمار اقتصادي و اجتماعي

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1395

ده،[106]ص.

ص.ع.به فارسي و انگليسي

سعيد پولادساز

دارد

ايرج كاظمي، ريحانه ريخته گران

1395/08/03

رياضي

ID10646

On the Optimality of some Block Designs Under a Mixed Interference Model Nafiseh Almasieh n almasieh@math iut ac ir 2016 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Saeid Pooladsaz spooladsaz@cc iut ac ir 2010 MSC 62K05 62K10 Keywords Circular weakly neighbor balanced designs D optimality E optimality Informationmatrix Interference model Left neighboring matrix Universal optimality AbstractThis thesis is an extension and generalization of the work done by Filipiak and R a ski 29 andFilipiak and Markiewicz 25 In many experiments the response to a treatment may be affected by other treatments appliedto neighboring experimental units Interference may contribute to variability in experimental resultsand lead to substantial losses in efficiency It is recommended then to use designs that are balancedin some sense with respect to neighbors In such experiments the interference model with neighboreffects is usually applied Such designs are applied for example in agriculture medicine etc Let Dt b k be the set of designs with t treatments b blocks and k experimental units per block Aninterference model with left neighbor effects associated with the design d Dt b k can be written as y Td Ld B where and are the vectors of treatment and block effects respectively while and are the vectors 2of random left neighbor effects and random errors respectively with E 0t Cov L It Thematrix B Ib 1k Td and Ld is the design matrix of block effects treatment effects and left neighboreffects respectively This model with random neighbor effects is called a mixed interference model In the theory of experimental designs the problem of determining optimal designs is often considered

سعيد پولادساز

ايرج كاظمي، ريحانه ريخته گران