2012/10/29 by Jérémie Bigot, Theofanis Sapatinas, Bigot, Jérémie +1
Computer Science · Mathematics · #Advanced Statistical Methods and Models #Image and Signal Denoising Methods #Statistical and numerical algorithms #math.ST #stat.TH
paper · pdf · doi:10.48550/arxiv.1210.7640
arxiv created 2012/10/31 · arxiv updated 2012/11/02
We consider the nonparametric estimation problem of time-dependent multivariate functions observed in a presence of additive cylindrical Gaussian white noise of a small intensity. We derive minimax lower bounds for the L2-risk in the proposed spatio-temporal model as the intensity goes to zero, when the underlying unknown response function is assumed to belong to a ball of appropriately constructed inhomogeneous time-dependent multivariate functions, motivated by practical applications. Furthermore, we propose both non-adaptive linear and adaptive non-linear wavelet estimators that are asymptotically optimal (in the minimax sense) in a wide range of the so-constructed balls of inhomogeneous time-dependent multivariate functions. The usefulness of the suggested adaptive nonlinear wavelet estimator is illustrated with the help of simulated and real-data examples.