mspeNERdb {saeMSPE}

Compute MSPE through double bootstrap(DB) method for Nested error regression model

Description

This function returns MSPE estimator with double bootstrap method for Nested error regression model.

Usage

mspeNERdb(ni, X, Y, Xmean, K = 50, C = 50, method = 1)

Arguments

ni

(vector). It represents the sample number for every small area.

X

(matrix). It represents the small area response.

Y

(vector). It represents the design matrix.

Xmean

(matrix). Stands for the population mean of auxiliary values.

K

(integer). It represents the first bootstrap sample number. Default value is 50.

C

(integer). It represents the second bootstrap sample number. Default value is 50.

method

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

Details

This method was proposed by P. Hall and T. Maiti. Double bootstrap method uses boostrap tool twice for NER model to avoid the unattractivitive bias correction: one is to estimate the estimator bias, the other is to correct for bias.

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 NER model.

bhat

(vector) Estimates of the unknown regression coefficients.

sigvhat2

(numeric) Estimates of the area-specific variance component.

sigehat2

(numeric) Estimates of the random error variance component.

Author(s)

Peiwen Xiao, Xiaohui Liu, Yuzi Liu, Jiming Jiang, and Shaochu Liu

References

F. B. Butar and P. Lahiri. On measures of uncertainty of empirical bayes small area estimators. Journal of Statistical Planning and Inference, 112(1-2):63-76, 2003.

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.

Peter Hall and T. Maiti. On parametric bootstrap methods for small area prediction. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 2006a.

H. T. Maiti and T. Maiti. Nonparametric estimation of mean squared prediction error in nested error regression models. Annals of Statistics, 34(4):1733-1750, 2006b.

Examples

### parameter setting 
Ni = 1000; sigmaX = 1.5; m = 10
beta = c(0.5, 1)
sigma_v2 = 0.8; sigma_e2 = 1
ni = sample(seq(1,10), m,replace = TRUE); n = sum(ni)
p = length(beta)
### population function
pop.model = function(Ni, sigmaX, beta, sigma_v2, sigma_e2, m){
  x = rnorm(m * Ni, 1, sqrt(sigmaX)); v = rnorm(m, 0, sqrt(sigma_v2)); y = numeric(m * Ni)
  theta = numeric(m); kk = 1
  for(i in 1 : m){
    sumx = 0
    for(j in 1:Ni){
      sumx = sumx + x[kk]
      y[kk] = beta[1] + beta[2] * x[kk] + v[i] + rnorm(1, 0, sqrt(sigma_e2))
      kk = kk + 1
    }
    meanx = sumx/Ni
    theta[i] = beta[1] + beta[2] * meanx + v[i]
  }
  group = rep(seq(m), each = Ni)
  x = cbind(rep(1, m*Ni), x)
  data = cbind(x, y, group)
  return(list(data = data, theta = theta))
} 
### sample function
sampleXY = function(Ni, ni, m, Population){
  Indx = c()
  for(i in 1:m){
    Indx = c(Indx, sample(c(((i - 1) * Ni + 1) : (i * Ni)), ni[i]))
  }
  Sample = Population[Indx, ]; Nonsample = Population[-Indx, ]
  return(list(Sample, Nonsample))
} 
### data generation process
Population = pop.model(Ni, sigmaX, beta, sigma_v2, sigma_e2, m)$data
XY = sampleXY(Ni, ni, m, Population)[[1]]
X = XY[, 1:p]
Y = XY[, p+1]
Xmean = matrix(NA, m, p)
for(tt in 1: m){
  Xmean[tt, ] = colMeans(Population[which(Population[,p+2] == tt), 1:p])
}
### mspe result
mspeNERdb(ni, X, Y, Xmean, 10, 10, method = 1)