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Update delta-method-demo.ipynb
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Zhuyi Xue authored Jun 4, 2024
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"id": "641cc613",
"metadata": {},
"source": [
"The Delta method: if $Y_n \\approx \\mathcal{N}\\left(\\mu, \\frac{\\sigma^2}{n} \\right)$, then $g(Y_n) \\approx \\mathcal{N}\\left(g(\\mu), \\left( g(\\mu)' \\right)^2\\frac{\\sigma^2}{n} \\right)$, given $g$ is differentiable and $g'(\\mu) \\neq 0$."
"The Delta method: if $Y_n \\sim \\mathcal{N}\\left(\\mu, \\frac{\\sigma^2}{n} \\right)$, then $g(Y_n) \\sim \\mathcal{N}\\left(g(\\mu), \\left( g(\\mu)' \\right)^2\\frac{\\sigma^2}{n} \\right)$, given $g$ is differentiable and $g'(\\mu) \\neq 0$."
]
},
{

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