ORTHONORMAL SERIES ESTIMATORS

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Focusing on advanced statistical methods, this book explores the approximation and estimation of nonparametric functions through projections onto orthonormal function bases. It introduces series estimators that enhance density estimators for various complex models, including mixture, deconvolution, and semi-parametric models. The authors demonstrate optimal convergence rates in Hilbert spaces and analyze mean square errors relative to basis size, utilizing cross-validation for consistent estimation. Additionally, wavelet estimators are examined within these frameworks, providing a comprehensive approach to modern data analysis techniques.