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International Journal of Statistika and Mathematika, ISSN: 2277- 2790 E-ISSN: 2249-8605
Volume 4, Issue 2, 2012 pp 47-49
Research Article
D – Optimal Design for Compound Poisson Regression Model
S. Joshua David1 and C. Santharam2
1,2 Department of Statistics, Loyola College, Chennai – 600034 (TN) INDIA.
Academic Editor: Dr. Dase R.K.
D- Optimality is one of the most commonly used design criteria for linear regression model. In industrial experiments binary or count data often arise, for example defective/non- defective or number of defects. For such data (GLMS) are appropriate Generalized Linear Models are especially useful for actuarial applications, since they allow estimate multiplicative models, and also allow forms of heteroscedasticity such as they are found frequently in actuarial problems, of Poisson-type, of gamma-type with a fixed coefficient of variation. An analogous D-optimality design criterion can be developed using asymptotic covariance matrix, for GLM, this matrix is a weighted version of the covariance matrix for the linear case, and the extension of existing D-optimality algorithm. We consider the problem of finding an optimal design under a compound Poisson regression model with a, any number of independent variables and a reciprocal link additive model linear predictor. Local D-optimality of a class of designs is established through use of a canonical form of the problem and a general equivalence theorem. The theorem is applied in conjunction with clustering techniques to obtain a fast method of finding designs that are robust to wide ranges of model parameter values.
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