{"paper":{"title":"Testing for Principal Component Directions under Weak Identifiability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Davy Paindaveine, Julien Remy, Thomas Verdebout","submitted_at":"2017-10-15T07:00:41Z","abstract_excerpt":"We consider the problem of testing, on the basis of a $p$-variate Gaussian random sample, the null hypothesis ${\\cal H}_0: {\\pmb \\theta}_1= {\\pmb \\theta}_1^0$ against the alternative ${\\cal H}_1: {\\pmb \\theta}_1 \\neq {\\pmb \\theta}_1^0$, where ${\\pmb \\theta}_1$ is the \"first\" eigenvector of the underlying covariance matrix and ${\\pmb \\theta}_1^0$ is a fixed unit $p$-vector. In the classical setup where eigenvalues $\\lambda_1>\\lambda_2\\geq \\ldots\\geq \\lambda_p$ are fixed, the Anderson (1963) likelihood ratio test (LRT) and the Hallin, Paindaveine and Verdebout (2010) Le Cam optimal test for this"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.05291","kind":"arxiv","version":3},"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"}