mspeFHlin {saeMSPE}

Compute MSPE through linearization method for Fay Herriot model

Description

This function returns MSPE estimator with linearization method for Fay Herriot model. These include the seminal Prasad-Rao method and its generalizations by Datta-Lahiri, Datta-Rao-Smith and Liu et.al. All these methods are developed for general linear mixed effects models.

Usage

mspeFHlin(Y, X, D, method = "PR", var.method = "default")

mspeFHPR(Y, X, D, var.method = "default")

mspeFHDL(Y, X, D, var.method = "default")

mspeFHDRS(Y, X, D, var.method = "default")

mspeFHMPR(Y, X, D, var.method = "default")

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 MSPE estimation method to be used. See "Details".

var.method

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

Details

Default method for mspeFHlin is "PR" ,proposed by N. G. N. Prasad and J. N. K. Rao, Prasad-Rao (PR) method uses Taylor series expansion to obtain a second-order approximation to the MSPE. Function mspeFHlin also provide the following methods:

Method "DL" proposed by Datta and Lahiri , It advanced PR method to cover the cases when the variance components are estimated by ML and REML estimator. Set method = "DL".

Method "DRS" proposed by Datta and Smith, It focus on the second order unbiasedness appoximation when the variance component is replaced by Empirical Bayes estimator. Set method = "DRS".

Method "MPR" is a modified version of "PR", It was proposed by Liu et al. It is a robust method that broaden the mean function from the linear form. Set method = "MPR".

Default var.method and available variance component estimation method for each method is list as follows:

For method = "PR", var.method = "MOM" is the only available variance component estimation method,

For method = "DL", var.method = "ML" or var.method = "REML" is available,

For method = "DRS", var.method = "EB" is the only available variance component estimation method,

For method = "MPR", var.method = "OBP" is the only available variance component estimation method.

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

N. G. N. Prasad and J. N. K. Rao. The estimation of the mean squared error of small-area estimators. Journal of the American Statistical Association, 85(409):163-171, 1990.

G. S. Datta and P. Lahiri. A unified measure of uncertainty of estimated best linear unbiased predictors in small area estimation problems. Statistica Sinica, 10(2):613-627, 2000.

G. S. Datta and R. D. D. Smith. On measuring the variability of small area estimators under a basic area level model. Biometrika, 92(1):183-196, 2005.

X. Liu, H. Ma, and J. Jiang. That prasad-rao is robust: Estimation of mean squared prediction error of observed best predictor under potential model misspecification. Statistica Sinica, 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))
mspeFHlin(Y,X,D,method = "PR", var.method = "default")