This data is generated based on heteroscedastic autoregressive multivariate Fay-Herriot model (model 3) by following these steps:
Generate sampling error e, random effect u, and auxiliary variables X1 X2.
For sampling error e, we set \(e\) ~ \(N_{3}(0, V_{e})\) , where \(V_{e} = (\sigma_{ij})_{i,j=1,2,3}\), with \(\sigma_{11}\) = 0.1 , \(\sigma_{22}\) = 0.2 , \(\sigma_{33}\) = 0.3 , and \(\rho_{e}\) = 0.5.
For random effect u, we set \(u\) ~ \(N_{3}(0, V_{u})\) , where \(\sigma_{u11}\) = 0.2 , \(\sigma_{u22}\) = 0.4 , \(\sigma_{u33}\) = 1.2, and \(\rho_{u}\) = 0.8.
For auxiliary variables X1 and X2, we set \(X1\) ~ \(N(5, 0.1)\) and \(X2\) ~ \(N(10, 0.2)\).
Calculate direct estimation Y1 Y2 and Y3 , where \(Y_{i}\) = \(X * \beta + u_{i} + e_{i}\). We take \(\beta_{1} = 5\) and \(\beta_{2} = 10\).
Auxiliary variables X1 X2, direct estimation Y1 Y2 Y3, and sampling variance-covariance v1 v2 v3 v12 v13 v23 are combined into a dataframe called datasae3.
datasae3A data frame with 50 rows and 11 variables:
Auxiliary variable of X1
Auxiliary variable of X2
Direct Estimation of Y1
Direct Estimation of Y2
Direct Estimation of Y3
Sampling Variance of Y1
Sampling Covariance of Y1 and Y2
Sampling Covariance of Y1 and Y3
Sampling Variance of Y2
Sampling Covariance of Y2 and Y3
Sampling Variance of Y3
Benavent, Roberto & Morales, Domingo. (2015). Multivariate Fay-Herriot models for small area estimation. Computational Statistics & Data Analysis. 100. 372-390. DOI: 10.1016/j.csda.2015.07.013.