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• W2272412902 abstract "ABSTRACTWe consider nonparametric estimation problems in the presence of dependent data, notably nonparametric regression with random design and nonparametric density estimation. The proposed estimation procedure is based on a dimension reduction. The minimax optimal rate of convergence of the estimator is derived assuming a sufficiently weak dependence characterised by fast decreasing mixing coefficients. We illustrate these results by considering classical smoothness assumptions. However, the proposed estimator requires an optimal choice of a dimension parameter depending on certain characteristics of the function of interest, which are not known in practice. The main issue addressed in our work is an adaptive choice of this dimension parameter combining model selection and Lepski's method. It is inspired by the recent work of Goldenshluger and Lepski [(2011), ‘Bandwidth Selection in Kernel Density Estimation: Oracle Inequalities and Adaptive Minimax Optimality’, The Annals of Statistics, 39, 1608–1632]..." @default.
• W2272412902 created "2016-06-24" @default.
• W2272412902 creator A5045471712 @default.
• W2272412902 creator A5060384161 @default.
• W2272412902 date "2017-09-05" @default.
• W2272412902 modified "2023-09-28" @default.
• W2272412902 title "Adaptive nonparametric estimation in the presence of dependence" @default.
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• W2272412902 doi "https://doi.org/10.1080/10485252.2017.1367788" @default.
• W2272412902 hasPublicationYear "2017" @default.
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