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

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  • Sakshi Arya

    (Pennsylvania State University)

  • Anuj Abhishek

    (UNC Charlotte)

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.

Suggested Citation

  • Sakshi Arya & Anuj Abhishek, 2023. "Adaptive Estimation of a Function from its Exponential Radon Transform in Presence of Noise," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(2), pages 1127-1155, August.
    • Handle: RePEc:spr:sankha:v:85:y:2023:i:2:d:10.1007_s13171-022-00300-8
    DOI: 10.1007/s13171-022-00300-8
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    References listed on IDEAS

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    1. Butucea, Cristina, 2000. "The adaptive rate of convergence in a problem of pointwise density estimation," Statistics & Probability Letters, Elsevier, vol. 47(1), pages 85-90, March.
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