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Activity Number:
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222
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Type:
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Contributed
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Date/Time:
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Monday, August 3, 2009 : 2:00 PM to 3:50 PM
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Sponsor:
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Biometrics Section
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| Abstract - #304285 |
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Title:
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Maximum Likelihood Estimation of Unconstrained Parameterization for the Covariance of Multivariate Longitudinal Data
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Author(s):
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Chulmin Kim*+
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Companies:
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Rochester Institute of Technology
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Address:
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School of Mathematical Sciences, Rochester, NY, 14623-5603,
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Keywords:
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Maximum likelihood estimation ; Covariance Structure ; Unconstrained parameterization ; Cholesky decomposition ; Longitudinal data
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Abstract:
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The positive-definiteness requirement for the covariance presents difficulties for modeling its structure. Pourahmadi proposed a parameterization of the covariance matrix for univariate longitudinal data where the parameters are unconstrained. To extend this idea to multivariate longitudinal data, we develop a modified Cholesky block decomposition that provides an unconstrained parameterization for the covariance matrix. To obtain maximum likelihood estimates for the parameters we derived the score functions and Fisher information. Their consistency and asymptotic normality are studied assuming that the observations are normally distributed. The likelihood ratio testing procedures for interesting hypotheses on the unconstrained parameters are developed. A real multivariate longitudinal data and a simulated data are given to illustrate the model introduced.
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