{"paper":{"title":"Predictor-dependent shrinkage for linear regression via partial factor modeling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Carlos Carvalho, P. Richard Hahn, Sayan Mukherjee","submitted_at":"2010-11-16T15:17:28Z","abstract_excerpt":"In prediction problems with more predictors than observations, it can sometimes be helpful to use a joint probability model, $\\pi(Y,X)$, rather than a purely conditional model, $\\pi(Y \\mid X)$, where $Y$ is a scalar response variable and $X$ is a vector of predictors. This approach is motivated by the fact that in many situations the marginal predictor distribution $\\pi(X)$ can provide useful information about the parameter values governing the conditional regression. However, under very mild misspecification, this marginal distribution can also lead conditional inferences astray. Here, we exp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.3725","kind":"arxiv","version":1},"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"}