## Nonparametric estimation of the singularities of a signal from noisy measurements

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- by A. I. Katsevich and A. G. Ramm
- Proc. Amer. Math. Soc.
**121**(1994), 1221-1234 - DOI: https://doi.org/10.1090/S0002-9939-1994-1227518-3
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## Abstract:

We study a problem of locating and estimating singularities of a signal measured with noise on a discrete set of points (fixed-design model). The signal consists of a smooth part with bounded first derivative and of finite number of singularities of the type $(x - {t_i})_ \pm ^p{d_i},0 \leq p \leq \frac {1}{2}$. The case $p = 0$ corresponds to a piecewise continuous function. The algorithm is based on convolving the data with a kernel having compact support. Optimal bandwidth of the kernel is calculated, the consistency of the algorithm is proved. The results of testing the proposed algorithm on model examples are presented.## References

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## Bibliographic Information

- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**121**(1994), 1221-1234 - MSC: Primary 62G05
- DOI: https://doi.org/10.1090/S0002-9939-1994-1227518-3
- MathSciNet review: 1227518