Arabidze, Dimitri Integral functionals of the Priestley-Chao regression function. (English) Zbl 1345.62063 Bull. Georgian Natl. Acad. Sci. (N.S.) 8, No. 2, 29-40 (2014). Summary: In the present paper the problem of statistical estimation of the nonlinear integral functional of a regression function is discussed. For the regression function and its derivatives well known Priestley-Chao estimator are taken. The problem is naturally considered in the Sobolev space. As an estimator for this function the plug-in estimatoris proposed. Theorems about consistency and asymptotically normality are proved. The order of the convergence is determined. The general methodology is used for some special cases. The estimation problem of Fisher’s information and Shannon entropy for Priestley-Chao’s regression function is solved. MSC: 62G07 Density estimation 62G20 Asymptotic properties of nonparametric inference 60F05 Central limit and other weak theorems Keywords:Priestley-Chao estimation; regression function; integral functional PDFBibTeX XMLCite \textit{D. Arabidze}, Bull. Georgian Natl. Acad. Sci. (N.S.) 8, No. 2, 29--40 (2014; Zbl 1345.62063) Full Text: Link