{"paper":{"title":"Linear regression estimation in non-linear single index models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Fadoua Balabdaoui, Gian-Andrea Thanei","submitted_at":"2016-12-22T17:10:20Z","abstract_excerpt":"In this article, we consider the problem of estimating the index parameter $\\alpha_0$ in the single index model $E[Y |X] = f_0(\\alpha_0^T X)$ with $f_0$ the unknown ridge function defined on $\\mathbb{R}$, $X$ a d-dimensional covariate and $Y$ the response. We show that when $X$ is Gaussian, then $\\alpha_0$ can be consistently estimated by regressing the observed responses $Y_i$, $i = 1, . . ., n$ on the covariates $X_1, . . ., X_n$ after centering and rescaling. The method works without any additional smoothness assumptions on $f_0$ and only requires that $cov(f_0(\\alpha_0^T X),\\alpha_0^TX) \\n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.07704","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"}