I am reading a paper "A note on the Delta Method" by Gary Oehlert, JASA, 1992.
I am trying to estimate the variance of a function of a random variable, but first I want to understand the limitations of using the Delta Method Taylor series.
when the function we are approximating is polynomially bounded in the random variables, then the naive Taylor series approximation will yield the correct asymptotic approximation..."
How can I tell if a function is polynomially bounded? Why is this a requirement of using the naive Taylor series approximation?
Is the alternative to a naive Taylor seires a higher-order Taylor series or a different approximation?
$^1$ p 28, middle of right col, last paragraph before Examples