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Machine Learning by Sergios Theodoridis

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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 Xsi27_e be a set of corresponding observations, Xsi28_e = {x1,x2,…,xN}. The corresponding joint pdf is parameterized in terms of the parameter vector θ211Dl. The log-likelihood is defined as,

L(θ)

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