Multivariate Cramér-Rao inequality for prediction and efficient predictors

Emmanuel Onzon

We derive and discuss a matricial Cramér-Rao type inequality for the quadratic prediction error matrix. A study of the attainment of the bound follows. Then we introduce an unbiased predictor for a bivariate Poisson process and prove that it is efficient, i.e. its quadratic error attains the Cramér-Rao bound.

Mots clés: Cramér-Rao inequality; Efficient predictor; Information inequality; Prediction; Fisher information; Parametric models

Domaines: Bio-informatique [q-bio.QM]; Bio-Informatique, Biologie Systémique [q-bio.QM]

Emmanuel Onzon. Multivariate Cramér-Rao inequality for prediction and efficient predictors. Statistics and Probability Letters, 2011, 81 (3), pp.429. ⟨10.1016/j.spl.2010.12.007⟩. ⟨hal-00719496⟩