var >= (grad psi)' I^(-1) (grad psi) is the Cramer-Rao lower bound in
its semiparametric form. Written this way it makes plain why the
bound depends only on the gradient of the functional and the
information operator, so a single information matrix serves every
functional of the model at once.
Usage
Ghosalsemiparaeff(grad_psi, info_matrix)
Arguments
- grad_psi
Gradient of the functional, length k.
- info_matrix
Information matrix, k by k and invertible.
Value
List with estimate (the bound), positive,
method.
Details
Formula: bound = g' I^(-1) g, obtained by solving I x = g.
References
Ghosal & van der Vaart (2017), Fundamentals of
Nonparametric Bayesian Inference, CUP, section 12.3.
Examples
Ghosalsemiparaeff(grad_psi = 5L, info_matrix = 5L)
#> $estimate
#> [1] 5
#>
#> $positive
#> [1] TRUE
#>
#> $method
#> [1] "semiparametric efficiency bound (GvdV 2017 sec. 12.3)"
#>
#> attr(,"class")
#> [1] "morie_rich_result" "list"
