I am reading the book Modelling Survival Data in Medical Research. The book says that it's the Taylor series approximation to the variance of a function of a random variable. I learnt Taylor expansion back in high school and as far as I could recollect from my memory, Taylor expansion basically says that the function could be approximated by a polynomial:
If expanding f(x) at x=0, the Taylor expansion of f(x) would look like:
I don't know exactly what o(1) is because I never got a chance to know more advanced maths, but I know at the limit 0(1) should approach to 0.
However, I am still quite blind in deriving the approximation of variance in this case. Could someone please show me the step? I explain my understanding in Taylor series because I was hoping someone could point out if I have misunderstood the theories or if there are other relevant and important theorems and knowledge in deriving the variance approximation. Many thanks!