{"paper":{"title":"On Affine and Conjugate Nonparametric Regression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Rajeshwari Majumdar","submitted_at":"2017-10-19T02:36:35Z","abstract_excerpt":"Suppose the nonparametric regression function of a response variable $Y$ on covariates $X$ and $Z$ is an affine function of $X$ such that the slope $\\beta$ and the intercept $\\alpha$ are real valued measurable functions on the range of the completely arbitrary random element $Z$. Assume that $X$ has a finite moment of order greater than or equal to $2$, $Y$ has a finite moment of conjugate order, and $\\alpha\\left(Z\\right)$ and $\\alpha\\left(Z\\right)X$ have finite first moments. Then, the nonparametric regression function equals the least squares linear regression function of $Y$ on $X$ with all"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.06987","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"}