mspeNERpb {saeMSPE}

Compute MSPE through parameter bootstrap method for Nested error regression model

Description

This function returns MSPE estimator with parameter bootstrap appoximation method for Nested error regression model

Usage

mspeNERpb(ni, X, Y, Xmean, K = 50, method = 4)

Arguments

ni

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

Y

(vector). It represents the response value for Nested error regression model.

X

(matrix). Stands for the available auxiliary values.

Xmean

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

K

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

method

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

Details

This method was proposed by Peter Hall and T. Maiti. Parametric bootstrap (pb) method uses bootstrap-based method to measure the accuracy of EB estimator. In this case, only EB estimator is available (method = 4).

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; K = 50; C = 50; 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
mspeNERpb(ni, X, Y, Xmean, 50)