{"paper":{"title":"Choosing the $p$ in $L_p$ loss: rate adaptivity on the symmetric location problem","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["stat.ME","stat.TH"],"primary_cat":"math.ST","authors_text":"Cun-Hui Zhang, Min Xu, Yu-Chun Kao","submitted_at":"2023-03-03T15:01:29Z","abstract_excerpt":"Given univariate random variables $Y_1, \\ldots, Y_n$ with the $\\text{Uniform}(\\theta_0 - 1, \\theta_0 + 1)$ distribution, the sample midrange $\\frac{Y_{(n)}+Y_{(1)}}{2}$ is the MLE for $\\theta_0$ and estimates $\\theta_0$ with error of order $1/n$, which is much smaller compared with the $1/\\sqrt{n}$ error rate of the usual sample mean estimator. However, the sample midrange performs poorly when the data has say the Gaussian $N(\\theta_0, 1)$ distribution, with an error rate of $1/\\sqrt{\\log n}$. In this paper, we propose an estimator of the location $\\theta_0$ with a rate of convergence that can"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.01992","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2303.01992/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}