# ASYMPTOTIC LAWS FOR CHANGE POINT ESTIMATION IN INVERSE REGRESSION

@article{Frick2014ASYMPTOTICLF, title={ASYMPTOTIC LAWS FOR CHANGE POINT ESTIMATION IN INVERSE REGRESSION}, author={Sophie Frick and Thorsten Hohage and Axel Munk}, journal={Statistica Sinica}, year={2014} }

We derive rates of convergence and asymptotic normality for the least squares estimator for a large class of parametric inverse regression models Y = (f )(X) +". Our theory provides a unied asymptotic tretament for estimation of f with discontinuities of certain order, including piecewise polynomials and piece- wise kink functions. Our results cover several classical and new examples, including splines with free knots or the estimation of piecewise linear functions with indirect observations…

## 5 Citations

Iterative Potts and Blake–Zisserman minimization for the recovery of functions with discontinuities from indirect measurements

- Computer ScienceProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2015

A new iterative minimization strategy for Blake–Zisserman as well as Potts functionals and a related jump-sparsity problem dealing with indirect, noisy measurements is proposed and a convergence analysis is provided.

Analysis of patchclamp recordings: model-free multiscale methods and software

- Computer ScienceEuropean biophysics journal : EBJ
- 2021

An operational manual how to use the model-free multiscale idealization methodology JSMURF, JULES, and HILDE available as an R-package and as a graphical user interface is provided.

Heterogeneous Multiscale Change-Point Inference and its Application to Ion Channel Recordings

- Computer Science
- 2018

Simulations and real data applications confirm that the proposed segmentation methods, JULES and JILTAD, estimate the underlying signal very accurately, even when events occur on small temporal scales, where the smoothing effect of the filter hinders estimation by common methods.

Fully Automatic Multiresolution Idealization for Filtered Ion Channel Recordings: Flickering Event Detection

- Computer ScienceIEEE Transactions on NanoBioscience
- 2018

A new model-free segmentation method, JULES, which combines recent statistical multiresolution techniques with local deconvolution for idealization of ion channel recordings and allows it to show that gramicidin A flickering events have the same amplitude as the slow gating events.

Jump-Penalized Least Absolute Values Estimation of Scalar or Circle-Valued Signals

- Computer Science, Mathematics
- 2017

The real-valued version of the Potts estimators improves upon the state-of-the-art solver w.r.t. to computational time, and the worst case complexity is improved for quantized data.

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