{"ID":2834587,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.01838","arxiv_id":"2512.01838","title":"Goodness-of-fit testing from observations with multiplicative measurement error","abstract":"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.","short_abstract":"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 un...","url_abs":"https://arxiv.org/abs/2512.01838","url_pdf":"https://arxiv.org/pdf/2512.01838v1","authors":"[\"Jan Johannes\",\"Bianca Neubert\"]","published":"2025-12-01T16:23:48Z","proceeding":"math.ST","tasks":"[\"math.ST\"]","methods":"[]","has_code":false}