## Theory of statistical inference and information |

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### Contents

Preface | 9 |

Convex functions of real variables | 39 |

Supplements and examples | 57 |

Copyright | |

15 other sections not shown

### Common terms and phrases

a-test Analogically arbitrary assume asymptotic Blackwell sufficient Borel subsets bounded classical sufficiency coincides conditional probability convergence convex functions convex set Corollary countable cr-finite measures Csiszar defined definition denote density differentiable disjoint distance distribution divergence dominated entropy equality equivalent equivariant estimation model Example exists follows from Proposition formula Halmos Hence holds identity implies inequality influence curve information theory integral isomorphy least favourable pair Lemma Let us consider Liese and Vajda likelihood ratio test limsup lower semicontinuous M-estimator Markov kernel measurable function measurable mapping measurable space measures on 3C metric space minimizes monotone nonempty nonnegative numbers obtains obviously present probability measures problem Proof properties Radon—Nikodym derivative random variables restriction result satisfies the condition satisfies the relation sense sequence signed measure statistical experiments stochastic strictly convex sub-cr-algebra Theorem tion topology unique vector weak gradient xe3C