mspeFHjack {saeMSPE}

Compute MSPE through Jackknife-based MSPE estimation method for Fay Herriot model

Description

This function returns MSPE estimator with jackknife method for Fay Herriot model.

Usage

mspeFHjack(Y, X, D, method = 1)

Arguments

Y

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

X

(matrix). It stands for the available auxiliary values.

D

(vector). Stands for the known sampling variances of each small area levels.

method

The variance component estimation method to be used. See "Details".

Details

This bias-corrected jackknife MSPE estimator was proposed by J. Jiang and L. S. M. Wan, it covers a fairly general class of mixed models which includes gLMM, mixed logistic model and some of the widely used mixed linear models as special cases.

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

M. H. Quenouille. Approximate tests of correlation in time series. Journal of the Royal Statistical Society. Series B (Methodological), 11(1):68-84, 1949.

J. W. Tukey. Bias and confidence in not quite large samples. Annals of Mathematical Statistics, 29(2):614, 1958.

J. Jiang and L. S. M. Wan. A unified jackknife theory for empirical best prediction with m estimation. Annals of Statistics, 30(6):1782-1810, 2002.

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))
mspeFHjack(Y, X, D, method = 1)