estimate.unknownsampvar {smallarea}R Documentation

Estimates of variance component, unknown sampling variance, regression coefficients and small area means in Fay Herriot model with unknown sampling variance.

Description

The function returns a list of 5 elements. The first element is an estimate of the variance component , the second element is an estimate of the parameter related to sampling variance, the third element is a vector of estimates of the regression coefficients in the Fay-Herriot model, the fourth element is a vector of the predictors pf the small area means and last element is the design matrix, the first column being a column of ones and the remaining columns represent the values of the covariates for different small areas. See details below.

Usage

estimate.unknownsampvar(response, mat.design, sample.size)

Arguments

response

A numeric vector. It represents the response or the direct survey based estimators in the Fay Herriot Model

mat.design

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.

sample.size

A numeric vector. The known sample sizes used to calculate the direct survey based estimators.

Details

For more details please see the package vignette.

Value

psi.hat

Estimate of the variance component

del.hat

Estimate of the parameter for sampling variance

beta.hat

Estimate of the unknown regression coefficients

theta.hat

Predictors of the small area means

mat.design

design matrix

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 fayherriot

Examples

set.seed( 55 )                  # setting a random seed
require(MASS)                   # the function mvrnorm requires MASS
x1 <- rep( 1, 10 )              # vector of ones representing intercept
x2 <- rnorm( 10 )               # vector of covariates randomly generated
x <- cbind( x1, x2 )            # design matrix
x <- as.matrix( x )             # coercing into class matrix
n <- rbinom (10, 20, 0.4)       # generating sample sizes for each small area
psi <- 1                        # true value of the psi parameter
delta <- 1                      # true value of the delta parameter
beta <- c( 1, 0.5 )             # true values of the regression parameters
theta <- mvrnorm( 1, as.vector( x %*% beta ), diag(10) )  # true small area means
y <- mvrnorm( 1, as.vector( theta ), diag( delta/n ) )  # design based estimators
estimate.unknownsampvar( y, x, n )      


[Package smallarea version 0.1 Index]