Bread for sandwiches
Computes the bread of the sandwich covariance matrix
## S3 method for class 'gmm' bread(x, ...) ## S3 method for class 'gel' bread(x, ...) ## S3 method for class 'tsls' bread(x, ...)
x |
A fitted model of class |
... |
Other arguments when |
When the weighting matrix is not the optimal one, the covariance matrix of the estimated coefficients is: (G'WG)^{-1} G'W V W G(G'WG)^{-1}, where G=d\bar{g}/dθ, W is the matrix of weights, and V is the covariance matrix of the moment function. Therefore, the bread is (G'WG)^{-1}, which is the second derivative of the objective function.
The method if not yet available for gel objects.
A k \times k matrix (see details).
Zeileis A (2006), Object-oriented Computation of Sandwich Estimators. Journal of Statistical Software, 16(9), 1–16. URL https://www.jstatsoft.org/v16/i09/.
# See \code{\link{gmm}} for more details on this example.
# With the identity matrix
# bread is the inverse of (G'G)
n <- 1000
x <- rnorm(n, mean = 4, sd = 2)
g <- function(tet, x)
{
m1 <- (tet[1] - x)
m2 <- (tet[2]^2 - (x - tet[1])^2)
m3 <- x^3 - tet[1]*(tet[1]^2 + 3*tet[2]^2)
f <- cbind(m1, m2, m3)
return(f)
}
Dg <- function(tet, x)
{
jacobian <- matrix(c( 1, 2*(-tet[1]+mean(x)), -3*tet[1]^2-3*tet[2]^2,0, 2*tet[2],
-6*tet[1]*tet[2]), nrow=3,ncol=2)
return(jacobian)
}
res <- gmm(g, x, c(0, 0), grad = Dg,weightsMatrix=diag(3))
G <- Dg(res$coef, x)
bread(res)
solve(crossprod(G))Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.