Cox and Poisson regression

Detailed notes on constructing restricted cubic spline

A simple review of Poisson regression

MGF, Laplace and Fourier

1.Laplace. 2. MGF, 3 Fourier

Statistical Errors in the Medical Literature

http://www.fharrell.com/2017/04/statistical-errors-in-medical-literature.html

Taylor series and Delta method

When X'X is invertible

X'X is always positive semidefinite, because for any nonzero a, a'X'Xa = (Xa)'(Xa) = ||Xa||² >= 0. Moreover, Xa = 0 (and hence ||Xa||² = 0) if and only if the columns of X are linearly dependent, so if X has full column rank then X'X is positive definite.

Every positive definite matrix is invertible, because if Ax=0 for x =/= 0 then x'Ax = dot(x, 0) = 0 which means A is not positive definite.

Therefore, if X has full column rank then X'X is invertible