saeME (version 1.3.1)

datamix: datamix

Description

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

1. Generate \(x_{1i}\) from a UNIF(5, 10) distribution, \(x_{2i}\) from a UNIF(9, 11) distribution, \(\psi_{i}\) = 3, \(c_{1i}\) = \(c_{2i}\) = 0.25, and \(\sigma_{v}^{2}\) = 2.

2. Generate \(u_{1i}\) from a N(0, \(c_{1i}\)) distribution, \(u_{2i}\) from a N(0, \(c_{2i}\)) distribution, \(e_{i}\) from a N(0, \(\psi_{i}\)) distribution, and \(v_{i}\) from a N(0, \(\sigma_{v}^{2}\)) distribution.

3. Generate \(x_{3i}\) from a UNIF(1, 5) distribution and \(x_{4i}\) from a UNIF(10, 14) distribution.

4. Generate \(\hat{x}_{1i}\) = \(x_{1i}\) + \(u_{1i}\) and \(\hat{x}_{2i}\) = \(x_{2i}\) + \(u_{2i}\).

5. Then for each iteration, we generated \(Y_{i}\) = \(2 + 0.5 \hat{x}_{1i} + 0.5 \hat{x}_{2i} + 2 x_{3i} + 0.5 x_{4i} + v_{i}\) and \(y_{i}\) = \(Y_{i} + e_{i}\).

This data contain combination between auxiliary variable measured with error and without error. Direct estimator y, auxiliary variable \(\hat{x}_{1}\) \(\hat{x}_{2}\) \(x_{3}\) \(x_{4}\), sampling variance \(\psi\), and \(c_{1} c_{2}\) are arranged in a dataframe called datamix.

Usage

data(datamix)

Format

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