Abstract

The asymptotic behaviour of an estimator of multiinformation (namely, the multiinformation of the empirical measure) is investigated. It is shown that it qualitatively depends on the value of a certain numerical characteristic. If this characteristic is non-zero then the estimator is asymtotically normally distributed. In the opposite case the asymptotic distribution of the estimator is the distribution of a weighted sum of squares of independent normally distributed random variables. A method how to find the respective weights is indicated.

AMS classification 62F12, 62E20, 94A17

Keywords

multiinformation

asymptotic behaviour

truncated product measure

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The paper builds on the work:

• Z. K. Lomicki and S. Z. Zaremba: The asymptotic distributions of estimators of the amount of transmitted information. Information and Control 2 (1959), n. 3, pp. 260-284.