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Delta method

{title2=$\sqrt n(\widehat\rho-\rho)$}

For a centered bivariate normal sample,
$$
\sqrt n(\widehat\rho-\rho)\xrightarrow dN\bigl(0,(1-\rho^2)^2\bigr).
$$
This is the multivariate delta method for $g(a,c,b)=c/\sqrt{ab}$.


Asymptotic distribution of the Gaussian sample correlation

Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 2 / 29K / d / Solution

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

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