This data generated by simulation based on Fay-Herriot with Measurement Error Model by following these steps:

Generate

*x1i*from a UNIF(5, 10) distribution,*x2i*from a UNIF(9, 11) distribution,*ψi*= 3,*c1i*=*c2i*= 0.25, and*σ2v*= 2.Generate

*u1i*from a N(0,*c1i*) distribution,*u2i*from a N(0,*c2i*) distribution,*ei*from a N(0,*ψi*) distribution, and*vi*from a N(0,*σ2v*) distribution.Generate

*x3i*from a UNIF(1, 5) distribution and*x4i*from a UNIF(10, 14) distribution.Generate

*x.hat1i*=*x1i*+*u1i*and*x.hat2i*=*x2i*+*u2i*.Then for each iteration, we generated

*Yi*=*2 + 0.5*x.hat1i + 0.5*x.hat2 i + 2*x3i + 0.5*x4i + vi*and*yi*=*Yi + ei*.

This data contain combination between auxiliary variable measured with error and without error.
Direct estimator `y`

, auxiliary variable *x.hat1* *x.hat2* *x3* *x4*, sampling variance *ψ*, and *c1 c2* are arranged in a dataframe called `datamix`

.

1 |

A data frame with 100 observations on the following 8 variables.

`small_area`

areas of interest.

`y`

direct estimator for each domain.

`x.hat1`

auxiliary variable (measured with error) for each domain.

`x.hat2`

auxiliary variable (measured with error) for each domain.

`x3`

auxiliary variable (measured without error) for each domain.

`x4`

auxiliary variable (measured without error) for each domain.

`vardir`

sampling variances for each domain.

`var.x1`

mean squared error of auxiliary variable and sorted as

`x.hat1`

`var.x2`

mean squared error of auxiliary variable and sorted as

`x.hat2`

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