Taylor Series

Definition

A way to approximate a function. For example, let’s say we have a function $f$ and let’s say we’re interested in approximating a function at point $a$ . This can be done by:

f (x) = f (a) + f^{'} (a) (x - a) + f^{″} (a) \frac{(x - a)^{2}}{2!} + f^{‴} (a) \frac{(x - a)^{3}}{3!}

Flavors

When it’s evaluated at 0 it’s called a Maclaurin series

Usage

Actually used for First order conditional estimation (FOCEI)