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Appendix B

# The delta method

The delta method is a statistical approach for deriving an approximate probability distribution for a function of an asymptotically normal estimator using the Taylor series approximation.

Let x = be a random variable asymptotically distributed as N(μ, σ2) with p.d.f. f(x), and g(x) be a single-valued function. If the integral $∫−∞+∞g(x)dF$ exists, it is called the mathematical expectation of g(x), denoted by E[g(x)]. The mean and variance of g(x) of the random variable x may not be readily obtainable. If x has the standard normal density, the integral corresponding to E[g(x)] does not have a tractable expression. In these ...

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