5 papers
Asymptotic equivalence for nonparametric regression with dependent errors: Gauss-Markov processes
Holger Dette, Martin Kroll
For the class of Gauss-Markov processes we study the problem of asymptotic equivalence of the nonparametric regression model with errors given by the increments of the process and…
Adaptive spectral density estimation by model selection under local differential privacy
Martin Kroll
We study spectral density estimation under local differential privacy. Anonymization is achieved through truncation followed by Laplace perturbation. We select our estimator from a…
Pointwise adaptive kernel density estimation under local approximate differential privacy
Martin Kroll
We consider non-parametric density estimation in the framework of local approximate differential privacy. In contrast to centralized privacy scenarios with a trusted curator, in th…
Local differential privacy: Elbow effect in optimal density estimation and adaptation over Besov ellipsoids
Cristina Butucea, Amandine Dubois, Martin Kroll +1
We address the problem of non-parametric density estimation under the additional constraint that only privatised data are allowed to be published and available for inference. For t…
Rate optimal estimation of quadratic functionals in inverse problems with partially unknown operator and application to testing problems
Martin Kroll
We consider the estimation of quadratic functionals in a Gaussian sequence model where the eigenvalues are supposed to be unknown and accessible through noisy observations only. Im…