11604

10653

كارشناسي ارشد

آمار

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1395

ده،[105]ص.: مصور،جدول،نمودار

ص.ع.به فارسي و انگليسي

سروش عليمرادي، ايرج كاظمي

ريحانه ريخته گران، زهرا صابري

1395/08/03

رياضي

ID10653

Robust estimation of the correlation matrix of longitudinal data Maryam Saeedi m saidi@math iut ac ir 2010 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Soruosh Alimoradi salimora@cc iut ac ir Supervisor Dr Iraj Kazemi i kazemi@stat ui ac ir 2010 MSC 62 07 62H20 62J05 Keywords Cholesky decomposition Correlation modeling Multivariate t Robustestimation Abstract An essential issue in the estimation of a covariance matrix in longitudinal data is itspositive de niteness This constraint creates a major obstacle and subsequently several al ternative techniques are introduced in the literature to take over the problem In this thesisa robust technique is addressed to develop the correlation matrix of the longitudinal data This is constructed upon the Cholesky decomposition of the underlying covariance matrix The technique is shown to be e ective in the analysis of longitudinal data in the sense thatthe positive de niteness of the estimated covariance is guaranteed It has also the uniquedistinction of providing an unconstrained and statistically meaningful re parameterization ofthe covariance matrix but at the expense of imposing an order among the underlying randomvariables The decomposition involves a positive de nite diagonal matrix proportional to the squareroot of diagonal entries of the covariance matrix and a unit lower triangular matrix to enable

سروش عليمرادي، ايرج كاظمي

ريحانه ريخته گران، زهرا صابري