Chesneau, Christophe; Kachour, Maher; Navarro, Fabien A note on the adaptive estimation of a quadratic functional from dependent observations. (English) Zbl 1420.62171 İstatistik 6, No. 1, 10-26 (2013). Summary: We investigate the estimation of the integral of the square of a multidimensional unknown function \(f\) under mild assumptions on the model allowing dependence on the observations. We develop an adaptive estimator based on a plug-in approach and wavelet projections. Taking the mean absolute error and assuming that \(f\) has a certain degree of smoothness, we prove that our estimator attains a sharp rate of convergence. Applications are given for the biased density model, the nonparametric regression model and a GARCH-type model under some mixing dependence conditions \((\alpha\)-mixing or \(\beta\)-mixing). A simulation study considering nonparametric regression models with dependent observations illustrates the usefulness of the proposed estimator. MSC: 62G08 Nonparametric regression and quantile regression 62G07 Density estimation 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) Keywords:quadratic functional estimation; plug-in approach; wavelets; rates of convergence; mixing dependence PDFBibTeX XMLCite \textit{C. Chesneau} et al., İstatistik 6, No. 1, 10--26 (2013; Zbl 1420.62171) Full Text: Link