Differentiability in quadratic mean

\(\int[(\sqrt{dP_t}-\sqrt{dP})/t - \tfrac12 g\sqrt{dP}]^2 \to 0\). Stated on the SQUARE ROOT of the density, which is what lets kinked families such as the Laplace qualify. Mirrors morie.fn.ksr061.

Usage

morie_dqm_check(density, score, t_grid = c(0.1, 0.05, 0.02, 0.01), theta = 0)

Arguments

density

function of (x, theta).

score

candidate score at theta.

t_grid

shrinking perturbations.

theta

base parameter.

Value

list: t_grid, dqm_integrals, shrinking, score_mean.

References

Kosorok (2008), Ch. 3.

Examples

morie_dqm_check(function(x, th) stats::dnorm(x, th), function(x) x)$shrinking
#> [1] TRUE