arXiv subjects

Bianca Neubert

Publications and source records attributed to Bianca Neubert.

3 recordsLinked to original sources

arXiv2026

Adaptive nonparametric regression from repeated measurements under common noise

We consider nonparametric estimation of the regression function in a model where individuals share a common noise component and repeated measurements are available for each individual. We propose a projection estimator which minimizes a least-squares contrast that accounts for the covariance structure resulting from the common noise. We analyze its risk measured either as the expectation of the empirical norm or as the expectation of the theoretical norm associated with the contrast. We discuss how the number of repeated measurements affects the estimation rates in the common noise model, and precisely characterize the dependence on the number of repetitions. In addition, we propose a data-driven projection estimator and establish risk bounds in terms of the expected empirical norm. The results are illustrated with some simulation experiments.

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arXiv2025

Goodness-of-fit testing from observations with multiplicative measurement error

Given observations from a positive random variable contaminated by multiplicative measurement error, we consider a nonparametric goodness-of-fit testing task for its unknown density in a non-asymptotic framework. We propose a testing procedure based on estimating a quadratic functional of the Mellin transform of the unknown density and the null. We derive non-asymptotic testing radii and testing rates over Mellin-Sobolev spaces, which naturally characterize regularity and ill-posedness in this model. By employing a multiple testing procedure with Bonferroni correction, we obtain data-driven procedures and analyze their performance. Compared with the non-adaptive tests, their testing radii deteriorate by at most a logarithmic factor. We illustrate the testing procedures with a simulation study using various choices of densities.

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arXiv2024

Quadratic functional estimation from observations with multiplicative measurement error

We consider the nonparametric estimation of the value of a quadratic functional evaluated at the density of a strictly positive random variable $X$ based on an iid. sample from an observation $Y$ of $X$ corrupted by an independent multiplicative error $U$. Quadratic functionals of the density covered are the $\mathbb{L}^2$-norm of the density and its derivatives or the survival function. We construct a fully data-driven estimator when the error density is known. The plug-in estimator is based on a density estimation combining the estimation of the Mellin transform of the $Y$ density and a spectral cut-off regularized inversion of the Mellin transform of the error density. The main issue is the data-driven choice of the cut-off parameter using a Goldenshluger-Lepski-method. We discuss conditions under which the fully data-driven estimator attains oracle-rates up to logarithmic deteriorations. We compute convergence rates under classical smoothness assumptions and illustrate them by a simulation study.

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