Approximations to nonlinear functions of random vectors
(Z Lu and M King)
Nonlinear functions of a random vector are often seen in statistical inference. Because it can be impossible in many situations to find their exact distributions, a Taylors expansion is then an attractive way of finding the approximating distributions.
This project investigates how the second order terms of Taylors expansion contribute to accuracy of the approximation.
In the terms of the Wald test, we argue that the non-invariance problems of the Wald test come from the inaccurate use of up to the first order terms only of the Taylors expansion. As a consequence, being proposed is a new Wald-type test for testing a nonlinear restriction by considering the second order term of the Taylors series expansion of the restriction function.
Like many tests, the test unfortunately involves nuisance parameters in many situations, which affects the performance of the test.