Problem of the Week
Hilton Memorial Lecture
Statistical Machine Learning Seminar
Hosted by Department of Mathematical Sciences
In regression models $Y=r(X)+\varepsilon$ with $X$ and $\varepsilon$ independent, the density of the response $Y$ can be estimated by a convolution of (kernel) estimators for the densities of $r(X)$ and $\varepsilon$. The rate of this convolution estimator depends on the smoothness of the densities of $X$ and $\varepsilon$ and on the smoothness and local flatness of the regression function $r$. When we observe the covariates $X$ with measurement errors, $Z=X+\eta$, we need deconvolution estimators for the densities of $X$ and $\varepsilon$ and for $r$. This is joint work with Anton Schick and Ursula U. Müller.