10244

9462

كارشناسي ارشد

آمار رياضي

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1393

78ص.

ص.ع. به فارسي و انگليسي

1396/10/02

كتابنامه

علوم رياضي

رياضي

ID9462

Optimal saturated block designs when observations are correlated Zahra Babaei z babaei@math iut ac ir 2015 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Saeid Pooladsaz spooladsaz@cc iut ac ir Advisor Dr Gholam Reza Omidi romidi@cc iut ac ir 2010 MSC 62k05 62k10 Keywords Saturated block designs Design optimality Majorization Ordinery and generalizedleast squeres Spatial correlation AbstractA block design setting is an integer triple v b k specifying the numbers of treatments blocks andexperimental units per block respectively available for an experiment If v k i e if it is not feasibleto have a single replication of every treatment in each block then v b k is called an incompleteblock design setting Consider comparing the relative e ectiveness of v tretments employing n bkexperimental units arranged in to b blocks of size k The standard linear model for the observationyju on unit u in block j when using designed is u 1 2 k yju d j u j ju j 1 2 bThe components of model are an overall mean the e ect d j u of treatment d j u assigned tounit u in block j by design d a block e ect j and a random error ju with zero mean Writ ing 1 2 v and 1 2 b for the vectors of treatment and block e ects andy y1 y2 yn for the responses vector then mean vector is E y 1n Md L forL Ib 1k the n b unit block design matrix for blocks and Md the n v unit treatment designmatrix for treatments It is well known that all treatment contrasts are estimble underd if and only ifthe information matrix for estimation of treatment e ects Cd Md I k 1 LL Md is of rank v 1 equivalently the rank of Xd 1n Md L is b v 1 A design with this property is said to beconnected A necessary condition ford to be connected is that the number of rows of Xd is at least

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