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Aaptivity; kernel estimation; minimax rates; Volterra equation; Laplace; convolution; FLUORESCENCE DECAY CURVES; ADAPTIVE DENSITY DECONVOLUTION; CONTRAST-ENHANCED MRI; NONPARAMETRIC DECONVOLUTION; WAVELET; DECONVOLUTION; OPTIMAL RATES; ANGIOGENESIS; CANCER; CT; REGULARIZATION; Statistics & Probability
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Laplace Deconvolution With Noisy Observations, Felix Abramovich, Marianna Pensky, Yves Rozenholc
Laplace Deconvolution With Noisy Observations, Felix Abramovich, Marianna Pensky, Yves Rozenholc
Faculty Bibliography 2010s
In the present paper we consider Laplace deconvolution for discrete noisy data observed on the interval whose length T-n may increase with a sample size. Although this problem arises in a variety of applications, to the best of our knowledge, it has been given very little attention by the statistical community. Our objective is to fill this gap and provide statistical treatment of Laplace deconvolution problem with noisy discrete data. The main contribution of the paper is explicit construction of an asymptotically rate-optimal (in the minimax sense) Laplace deconvolution estimator which is adaptive to the regularity of the unknown function. …