WAVELET ESTIMATION OF REGRESSION DERIVATIVES FOR BIASED AND NEGATIVELY ASSOCIATED DATA

• Published in: Revstat Vol. 20; no. 3; p. 353
• Main Authors: Kou, Junke, Chesneau, Christophe
• Format: Journal Article
• Language: English
• Published: Instituto Nacional de Estatistica 01.07.2022; Instituto Nacional de Estatística | Statistics Portugal
• Subjects: Lp risk; negatively associated; Regression derivatives estimation; wavelets
• ISSN: 1645-6726; 2183-0371
• DOI: 10.57805/revstat.v20i3.375

* This paper considers the estimation of the derivatives of a regression function based on biased data. The main feature of the study is to explore the case where the data comes from a negatively associated process. In this context, two different wavelet estimators are introduced: a linear wavelet estimator and a nonlinear wavelet estimator using the hard thresholding rule. Their theoretical performance is evaluated by determining sharp rates of convergence under [L.sup.p] risk, assuming that the unknown function of interest belongs to a ball of Besov spaces [B.sub.p,q.sup.s] (R). The obtained results extend some existing works on biased data in the independent case to the negatively associated case. Keywords: * regression derivatives estimation; negatively associated; Lp risk; wavelets. AMS Subject Classification: * 62G07, 62G20, 42C40.