Machine Learning

Appendix B

Probability Theory and Statistics

Chapter Outline

B.1 Cramér-Rao Bound 1019

B.2 Characteristic Functions 1020

B.3 Moments and Cumulants 1020

B.4 Edgeworth Expansion of a pdf 1021

Reference 1022

B.1 Cramér-Rao Bound

Let x denote a random vector and let $\mathcal{X}$ be a set of corresponding observations, $\mathcal{X}$ = {x₁,x₂,…,x_N}. The corresponding joint pdf is parameterized in terms of the parameter vector θ ∈ ^l. The log-likelihood is defined as,

$L(\mathit{\theta })$