fayherriot {smallarea}

Estimate of the variance component in Fay Herriot Model using Fay Herriot Method

Description

This function returns a list with one element in it which is the estimate of the variance component in the Fay Herriot Model. The estimate is found by solving an equation (for details see vignette) and is due to Fay Herriot. The uniroot in the stats package is used to find the root. uniroot searches for a root of that equation in a particular interval the lower bound is 0 and the upper bound is set to estimate of the variance component using Prasad Rao method + three times the square root of the number of observation. It depends on the function prasadraoest in the same package. Note that our function does not accept missing values.

Usage

fayherriot(response, designmatrix, sampling.var)

Arguments

response

a numeric vector. It represents the response or the observed value in the Fay Herriot Model

designmatrix

a numeric matrix. The first column is a column of ones(also called the intercept). The other columns consist of observations of each of the covariates or the explanatory variable in Fay Herriot Model.

sampling.var

a numeric vector consisting of the known sampling variances of each of the small area levels.

Details

For more details please see the attached vignette

Value

estimate

estimate of the variance component

Author(s)

Abhishek Nandy

References

On measuring the variability of small area estimators under a basic area level model. Datta, Rao, Smith. Biometrika(2005),92, 1,pp. 183-196 Large Sample Techniques for Statistics, Springer Texts in Statistics. Jiming Jiang. Chapters - 4,12 and 13.

See Also

prasadraoest maximlikelihood resimaxilikelihood

Examples

response=c(1,2,3,4,5)
designmatrix=cbind(c(1,1,1,1,1),c(1,2,4,4,1),c(2,1,3,1,5))
randomeffect.var=c(0.5,0.7,0.8,0.4,0.5)
fayherriot(response,designmatrix,randomeffect.var)