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Information Loss Due to the Data Reduction of Sample Data from Discrete Distributions

Author

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  • Maryam Moghimi

    (Center on Stochastic Modeling, Optimization, and Statistics (COSMOS), the University of Texas at Arlington, Arlington, TX 76013, USA
    This paper was part of the author’s doctoral dissertation of May 2020.
    The two authors contributed equally to this paper.)

  • Herbert W. Corley

    (Center on Stochastic Modeling, Optimization, and Statistics (COSMOS), the University of Texas at Arlington, Arlington, TX 76013, USA
    The two authors contributed equally to this paper.)

Abstract

In this paper, we study the information lost when a real-valued statistic is used to reduce or summarize sample data from a discrete random variable with a one-dimensional parameter. We compare the probability that a random sample gives a particular data set to the probability of the statistic’s value for this data set. We focus on sufficient statistics for the parameter of interest and develop a general formula independent of the parameter for the Shannon information lost when a data sample is reduced to such a summary statistic. We also develop a measure of entropy for this lost information that depends only on the real-valued statistic but neither the parameter nor the data. Our approach would also work for non-sufficient statistics, but the lost information and associated entropy would involve the parameter. The method is applied to three well-known discrete distributions to illustrate its implementation.

Suggested Citation

  • Maryam Moghimi & Herbert W. Corley, 2020. "Information Loss Due to the Data Reduction of Sample Data from Discrete Distributions," Data, MDPI, vol. 5(3), pages 1-18, September.
    • Handle: RePEc:gam:jdataj:v:5:y:2020:i:3:p:84-:d:413006
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    References listed on IDEAS

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    1. Frank Arute & Kunal Arya & Ryan Babbush & Dave Bacon & Joseph C. Bardin & Rami Barends & Rupak Biswas & Sergio Boixo & Fernando G. S. L. Brandao & David A. Buell & Brian Burkett & Yu Chen & Zijun Chen, 2019. "Quantum supremacy using a programmable superconducting processor," Nature, Nature, vol. 574(7779), pages 505-510, October.
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