mspeFHsumca {saeMSPE}

Compute MSPE through Sumca method for Fay Herriot model

Description

This function returns MSPE estimator with the combination of linearization and resampling appoximation method called "Sumca", for Fay Herriot model.

Usage

mspeFHsumca(Y, X, D, K = 50, method = 1)

Arguments

Y

(vector). It represents the response value for Fay Herriot model.

X

(matrix). Stands for the available auxiliary values.

D

(vector). It represents the knowing sampling variance for Fay Herriot model.

K

(integer). It represents the Monte-Carlo sample size for "Sumca". Default value is 50.

method

It represents the variance component estimation method. See "Details".

Details

This method was proposed by J. Jiang, P. Lahiri, and T. Nguyen, sumca method combines the advantages of linearization and resampling methods and obtains unified, positive, low-computation burden and second-order unbiased MSPE estimators.

Default value for method is 1, method = 1 represents the MOM method , method = 2 and method = 3 represents ML and REML method, respectively.

Value

This function returns a list with components:

MSPE

(vector) MSPE estimates for Fay Herriot model.

bhat

(vector) Estimates of the unknown regression coefficients.

Ahat

(numeric) Estimates of the variance component.

Author(s)

Peiwen Xiao, Xiaohui Liu, Yuzi Liu, Jiming Jiang, and Shaochu Liu

References

J. Jiang and M. Torabi. Sumca: simple; unified; monte carlo assisted approach to second order unbiased mean squared prediction error estimation. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 82(2):467-485, 2020.

Examples

X = matrix(runif(10 * 3), 10, 3)
X[,1] = rep(1, 10) 
D = (1:10) / 10 + 0.5
Y = X %*% c(0.5,1,1.5) + rnorm(10, 0, sqrt(2)) + rnorm(10, 0, sqrt(D))
mspeFHsumca(Y, X, D, K = 50, method = 1)