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Comparison of Statistical Experiments
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  • Cited by 51
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    This book has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Gushchin, Alexander Kordzakhia, Nino and Novikov, Alexander 2018. Translation invariant statistical experiments with independent increments. Statistical Inference for Stochastic Processes, Vol. 21, Issue. 2, p. 363.

    Williams, Katherine S. Secomb, Timothy W. and El-Kareh, Ardith W. 2018. Additive Damage Models for Cellular Pharmacodynamics of Radiation–Chemotherapy Combinations. Bulletin of Mathematical Biology, Vol. 80, Issue. 5, p. 1236.

    Pujol, J. 2018. Comment on “Unbiased Estimation of Moment Magnitude from Body‐ and Surface‐Wave Magnitudes,” by R. Das, H. R. Wason, and M. L. Sharma, and “Comparative Analysis of Regression Methods Used for Seismic Magnitude Conversions” by P. Gasperini, B. Lolli, and S. Castellaro. Bulletin of the Seismological Society of America, Vol. 108, Issue. 1, p. 533.

    Das, Ranjit Wason, H. R. Gonzalez, Gabriel Sharma, M. L. Choudhury, Deepankar Lindholm, Conrad Roy, Narayan and Salazar, Pablo 2018. Earthquake Magnitude Conversion Problem. Bulletin of the Seismological Society of America, Vol. 108, Issue. 4, p. 1995.

    Horodecki, Michał Oppenheim, Jonathan and Sparaciari, Carlo 2018. Extremal distributions under approximate majorization. Journal of Physics A: Mathematical and Theoretical, Vol. 51, Issue. 30, p. 305301.

    Nasser, Rajai 2017. Topological structures on DMC spaces. p. 3175.

    Taheri, Seyed Mohammad Mahyar, Hamidreza Firouzi, Mohammad Ghalebi K., Elahe Grosu, Radu and Movaghar, Ali 2017. HellRank: a Hellinger-based centrality measure for bipartite social networks. Social Network Analysis and Mining, Vol. 7, Issue. 1,

    Buscemi, Francesco and Gour, Gilad 2017. Quantum relative Lorenz curves. Physical Review A, Vol. 95, Issue. 1,

    Gushchin, Alexander A. and Borzykh, Dmitriy A. 2017. Integrated quantile functions: properties and applications. Modern Stochastics: Theory and Applications, Vol. 4, Issue. 4, p. 285.

    Bandyopadhyay, Saptarshi Chung, Soon-Jo and Hadaegh, Fred Y. 2017. Probabilistic and Distributed Control of a Large-Scale Swarm of Autonomous Agents. IEEE Transactions on Robotics, Vol. 33, Issue. 5, p. 1103.

    Kuramochi, Yui 2017. Minimal sufficient statistical experiments on von Neumann algebras. Journal of Mathematical Physics, Vol. 58, Issue. 6, p. 062203.

    Buscemi, Francesco 2017. Comparison of noisy channels and reverse data-processing theorems. p. 489.

    Jencova, Anna 2016. Comparison of quantum channels and statistical experiments. p. 2249.

    Buscemi, Francesco and Datta, Nilanjana 2016. Equivalence between divisibility and monotonic decrease of information in classical and quantum stochastic processes. Physical Review A, Vol. 93, Issue. 1,

    Buscemi, F. 2016. Degradable channels, less noisy channels, and quantum statistical morphisms: An equivalence relation. Problems of Information Transmission, Vol. 52, Issue. 3, p. 201.

    Gushchin, A. A. 2016. The minimum increment of f-divergences given total variation distances. Mathematical Methods of Statistics, Vol. 25, Issue. 4, p. 304.

    Raginsky, Maxim 2016. Channel polarization and Blackwell measures. p. 56.

    Bandyopadhyay, Saptarshi Soon-Jo Chung and Hadaegh, Fred Y. 2016. A probabilistic eulerian approach for motion planning of a large-scale swarm of robots. p. 3822.

    Renes, Joseph M. 2016. Relative submajorization and its use in quantum resource theories. Journal of Mathematical Physics, Vol. 57, Issue. 12, p. 122202.

    Javidi, Tara 2016. Information acquisition and sequential belief refinement. p. 7635.

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Book description

There are a number of important questions associated with statistical experiments: when does one given experiment yield more information than another; how can we measure the difference in information; how fast does information accumulate by repeating the experiment? The means of answering such questions has emerged from the work of Wald, Blackwell, LeCam and others and is based on the ideas of risk and deficiency. The present work which is devoted to the various methods of comparing statistical experiments, is essentially self-contained, requiring only some background in measure theory and functional analysis. Chapters introducing statistical experiments and the necessary convex analysis begin the book and are followed by others on game theory, decision theory and vector lattices. The notion of deficiency, which measures the difference in information between two experiments, is then introduced. The relation between it and other concepts, such as sufficiency, randomisation, distance, ordering, equivalence, completeness and convergence are explored. This is a comprehensive treatment of the subject and will be an essential reference for mathematical statisticians.

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