In statistics, the delta method is a technique for deriving the asymptotic distribution of a random variable, applicable when that variable can be defined as a differentiable function of another random variable that is itself asymptotically Gaussian. More generally, the method extends to functionals of stochastic processes that are Hadamard directionally differentiable and converge to a limiting process.
Facts
StatementIf a sequence of random variables Xn satisfies the square root of n times (Xn minus theta) converging in distribution to a normal distribution with mean 0 and variance sigma squared, then for a differentiable function g the square root of n times (g(Xn) minus g(theta)) converges in distribution to a normal distribution with mean 0 and variance sigma squared times g prime of theta squared. 1 Sources
1. Delta method, Wikipedia
Univariate delta method sectionQuote, Univariate delta method section
if there is a sequence of random variables Xn satisfying square root of n [Xn - theta] converges in distribution to N(0, sigma^2), then square root of n [g(Xn) - g(theta)] converges in distribution to N(0, sigma^2 * [g'(theta)]^2)
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