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- W2341289087 abstract "Waclawiw and Liang (1993) develop an estimating function-based approach to component estimation in the generalized linear mixed model with univariate random effects and a vector of fixed effects. In their approach they utilize the standard optimal estimating functions to estimate the fixed effects and a so-called Stein-type form of estimating functions to estimate both the random effects and their variance. In this paper, we provide a semiparametric solution to the estimation problem dealt by Waclawiw and Liang. The solution is obtained under two set-up by utilizing the standard theory of optimal estimating functions (Godambe and Thompson, 1989). Under the first set-up, the solution is obtained in three steps. In the first step, the estimating functions for the regression parameters, and the random effects are developed by treating the random effects as fixed effects. In the second step, we obtain the prediction of the random effects by taking their true nature of randomness into account. These predicted random effects are then used in the estimating equations for the regression parameters, of Step 1, to obtain their improved estimates. In the third step, the estimating function for the variance of the random effects is developed based on the true nature of the random effects. Under the second set-up, the estimating functions for the regression parameters, random effects and their variance are developed by utilizing the true nature of the random effects directly. Results of a small simulation study based on the performance of the proposed estimating function-based approaches are reported." @default.
- W2341289087 created "2016-06-24" @default.
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- W2341289087 date "2016-01-01" @default.
- W2341289087 modified "2023-09-27" @default.
- W2341289087 title "Institute of Mathematical Statistics LECTURE NOTES ? MONOGRAPH SERIES" @default.
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