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Activity Number:
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362
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Type:
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Contributed
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Date/Time:
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Wednesday, August 6, 2003 : 10:30 AM to 12:20 PM
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Sponsor:
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Section on Statistics & the Environment
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| Abstract - #301804 |
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Title:
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Analysis of Censored Environmental Data with Box-Cox Transformations
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Author(s):
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Reza Modarres*+ and Jade L. Freeman
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Companies:
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George Washington University and
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Address:
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2201 G St. NW-Room 315, Washington, DC, 20052-0001,
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Keywords:
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EM algorithm ; censored data ; confidence region ; Box-Cox transformation
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Abstract:
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We present a method for estimating the mean vector from a multivariate skew distribution that includes some unobserved data below the detection limits. The method uses a Box-Cox transformation, of which the parameters are found by maximizing the likelihood function over a fixed power transformation set. To estimate the mean vector and the covariance matrix, we develop an EM algorithm solution and use it to maximize the likelihood. We study the effects of an incorrect transformation on the conditional expectations and imputed values. Given a transformation, we obtain expressions for the mean vector, covariance matrix, and the asymptotic covariance of the vector of means in the original scale. Expressions are obtained for a confidence region for the vector of means. The performance of the MLE method in selecting the correct power transformation and the coverage rate of the confidence region under several conditions are investigated in a simulation study. This method gives reliable results for finding effective transformations and the coverage rate for highly skew datasets. The method is applied to a dataset collected to monitor water quality.
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