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… 

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