geex (version 1.1.1)

estimate_sandwich_matrices: Estimate component matrices of the empirical sandwich covariance estimator

Description

For a given set of estimating equations computes the 'meat' (\(B_m\) in Stefanski and Boos notation) and 'bread' (\(A_m\) in Stefanski and Boos notation) matrices necessary to compute the covariance matrix.

Usage

estimate_sandwich_matrices(.basis, .theta)

Value

a sandwich_components object

Arguments

.basis

basis an object of class m_estimation_basis

.theta

vector of parameter estimates (i.e. estimated roots)

Details

For a set of estimating equations (\(\sum_i \psi(O_i, \theta) = 0\)), this function computes:

$$A_i = \partial \psi(O_i, \theta)/\partial \theta$$

$$A = \sum_i A_i$$

$$B_i = \psi(O_i, \theta)\psi(O_i, \theta)^T$$

$$B = \sum_i B_i$$

where all of the above are evaluated at \(\hat{\theta}\). The partial derivatives in \(A_i\) numerically approximated by the function defined in deriv_control.

Note that \(A = \sum_i A_i\) and not \(\sum_i A_i/m\), and the same for \(B\).

References

Stefanski, L. A., & Boos, D. D. (2002). The calculus of m-estimation. The American Statistician, 56(1), 29-38.

Examples

myee <- function(data){
  function(theta){
    c(data$Y1 - theta[1],
     (data$Y1 - theta[1])^2 - theta[2])
   }
 }

# Start with a basic basis
mybasis <- create_basis(
  estFUN = myee,
  data   = geexex)

# Now estimate sandwich matrices
estimate_sandwich_matrices(
 mybasis, c(mean(geexex$Y1), var(geexex$Y1)))