{"paper":{"title":"Second Order Correctness of Perturbation Bootstrap M-Estimator of Multiple Linear Regression Parameter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ME","stat.TH"],"primary_cat":"math.ST","authors_text":"Debraj Das, Soumendra Nath Lahiri","submitted_at":"2016-05-04T21:22:50Z","abstract_excerpt":"Consider the multiple linear regression model $y_{i} = \\boldsymbol{x}'_{i} \\boldsymbol{\\beta} + \\epsilon_{i}$, where $\\epsilon_i$'s are independent and identically distributed random variables, $\\mathbf{x}_i$'s are known design vectors and $\\boldsymbol{\\beta}$ is the $p \\times 1$ vector of parameters. An effective way of approximating the distribution of the M-estimator $\\boldsymbol{\\bar{\\beta}}_n$, after proper centering and scaling, is the Perturbation Bootstrap Method. In this current work, second order results of this non-naive bootstrap method have been investigated. Second order correctn"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.01440","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":""},"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"}