Delta method

n (T_{n} - θ)

is asymptotically normal, differentiability gives

n (g (T_{n}) - g (θ))

the variance multiplied by

g^{'} (θ)^{2}

Table of contents
- Functional delta method Delta method
- Asymptotic distribution of the Gaussian sample correlation Delta method

Functional delta method ( $r_{n} (Φ (X_{n}) - Φ (s)) d \dot{Φ}_{s} (X)$ )

 0  0

r_{n} (X_{n} - s)

converges in distribution to

X

and

Φ

is Hadamard differentiable at

s

tangentially to a space containing the limit, the displayed transformation rule holds under the usual measurability and tight separable-support conditions. The variables

X_{n}

must belong to the domain of

Φ

Asymptotic distribution of the Gaussian sample correlation ( $n (ρ - ρ)$ )

 0  0

For a centered bivariate normal sample,

n (ρ - ρ) d N (0, (1 - ρ^{2})^{2}) .

(1)

This is the multivariate delta method for

g (a, c, b) = c / ab

 Ancestors (6)

 Incoming links (32)

 View article source

 Discussion (0)

New discussion

There are no discussions about this article yet.

 Articles by others on the same topic (1)

Delta method by

Wikipedia Bot  1

 Read the full article

  See all articles in the same topic Create my own version