kb:delta_method

Delta method

The Delta method is used to calculate the asymptotic variance of a random variable that is a function of another random variable. The derivative of the function and the mean and asymptotic variance of the second RV are used.

Let Zn be a sequence of random variables such that

n(Znθ)(d)nN(0,σ2)

where σ2 is the asymptotic variance, and θR. This means that Zn is asymptotically normal.

Given a function g:RR that is continuously differentiable at θ,

  • g(Zn)(P)ng(θ)
  • (g(Zn))n1 is also asymptotically normal with asymptotic variance g(θ)2σ2
  • In other words,

n(g(Zn)g(θ))(d)nN(0,g(θ)2σ2)

  • kb/delta_method.txt
  • Last modified: 2024-04-30 04:03
  • by 127.0.0.1