Èl’Basioniĭ, A. Kh. On the convergence of functionals of a statistical estimate of entropy in a polynomial scheme. (English. Russian original) Zbl 0632.62017 Theory Probab. Math. Stat. 33, 127-133 (1986); translation from Teor. Veroyatn. Mat. Stat. 33, 113-120 (1985). Summary: Functional limit theorems for random processes generated by a statistical estimate of entropy in a polynomial scheme are proved. A Wiener measure is used as the limit under the conditions considered. MSC: 62E20 Asymptotic distribution theory in statistics 60F17 Functional limit theorems; invariance principles 62F12 Asymptotic properties of parametric estimators 60B10 Convergence of probability measures 60B12 Limit theorems for vector-valued random variables (infinite-dimensional case) 62M09 Non-Markovian processes: estimation Keywords:Functional limit theorems; estimate of entropy; polynomial scheme; Wiener measure PDFBibTeX XMLCite \textit{A. Kh. Èl'Basioniĭ}, Theory Probab. Math. Stat. 33, 127--133 (1986; Zbl 0632.62017); translation from Teor. Veroyatn. Mat. Stat. 33, 113--120 (1985)