# Estimates of variance component, unknown sampling variance, regression coefficients and small area means in Fay Herriot model with unknown sampling variance. 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. ```r 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. ## Returns - **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 ## 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. ## Author(s) Abhishek Nandy ## See Also `prasadraoest` `fayherriot` ## Examples ```r 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 ) ```

estimate.unknownsampvar function