Additive inverse regression models with convolution-type operators
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Date
2013-03-14
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Abstract
In a recent paper Birke and Bissantz (2008) considered the problem of nonparametric estimation in inverse regression models with convolution-type operators. For multivariate predictors
nonparametric methods suff er from the curse of dimensionality and we consider inverse re-
gression models with the additional qualitative assumption of additivity. In these models
several additive estimators are studied. In particular, we investigate estimators under the
random design assumption which are applicable when observations are not available on a
grid. Finally, we compare this estimator with the marginal integration and the non-additive
estimator by means of a simulation study. It is demonstrated that the new method yields a
substantial improvement of the currently available procedures.
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Keywords
additive models, convolution-type operators, inverse regression