Adaptive Estimation of a Function from its Exponential Radon Transform in Presence of Noise

Sakshi Arya () and Anuj Abhishek ()
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Sakshi Arya: Pennsylvania State University
Anuj Abhishek: UNC Charlotte

Sankhya A: The Indian Journal of Statistics, 2023, vol. 85, issue 2, No 2, 1127-1155

Abstract: Abstract In this article we propose a locally adaptive strategy for estimating a function from its Exponential Radon Transform (ERT) data, without prior knowledge of the smoothness of functions that are to be estimated. We build a non-parametric kernel type estimator and show that for a class of functions comprising a wide Sobolev regularity scale, our proposed strategy follows the minimax optimal rate up to a log n $\log {n}$ factor. We also show that there does not exist an optimal adaptive estimator on the Sobolev scale when the pointwise risk is used and in fact the rate achieved by the proposed estimator is the adaptive rate of convergence.

Keywords: Adaptive estimation; exponential radon transform.; Primary 62G05; Secondary 44A12 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s13171-022-00300-8

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