mspeFHdb {saeMSPE}

Compute MSPE through double bootstrap method for Fay Herriot model

Description

This function returns MSPE estimate with double bootstrap appoximation method for Fay Herriot model.

Usage

mspeFHdb(Y, X, D, K = 50, C = 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 first bootstrap sample number. Default value is 50.

C

(integer). It represents the second bootstrap sample number. Default value is 50.

method

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

Details

This method was proposed by P. Hall and T. Maiti. Double bootstrap method uses boostrap tool twice for Fay Herriot model to avoid the unattractivitive bias correction: one is to estimate the estimator bias, the other is to correct for bias.

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

Value

A list with components:

MSPE

(vector) MSPE estimate based on double bootstrap method.

bhat

(vector) estimate of the unknown regression coefficients.

Ahat

(numeric) estimate of the variance component.

Author(s)

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

References

P. Hall and T. Maiti. On parametric bootstrap methods for small area prediction. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 2006.

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))
mspeFHdb(Y, X, D, K = 10, C = 10, 1)