Functional delta method with its remainder

\(r_n(\phi(X_n) - \phi(\theta)) \Rightarrow \phi'_\theta(X)\). The remainder is RETURNED rather than assumed to be o_P(1), so a non-differentiable phi is visible. Mirrors morie.fn.ksr042.

Usage

morie_functional_delta(phi, X_n, theta, r_n)

Arguments

phi

functional.

X_n

statistic value.

theta

centring value.

r_n

scaling rate.

Value

list: scaled_increment, linear_approximation, remainder, derivative.

References

Kosorok (2008), Ch. 2.

Examples

morie_functional_delta(function(z) z^2, 2.01, 2, 100)$remainder
#> [1] 0.01