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On the asymptotic distribution of useful Shannon entropy in a stratified sampling. (English) Zbl 0829.62009

Summary: The useful Shannon entropy introduced by C. F. Picard [Graphes et questionnaires. (1972; Zbl 0266.94018)] is considered, and the asymptotic distribution of its analogue estimator, in a stratified sampling, is obtained. Also, on the basis of these results, tests of hypotheses are constructed.

MSC:

62B10 Statistical aspects of information-theoretic topics
62E20 Asymptotic distribution theory in statistics
62D05 Sampling theory, sample surveys
62F03 Parametric hypothesis testing