{"76641":{"#nid":"76641","#data":{"type":"event","title":"Statistics Seminar - Non-sparse methods for out-of-sample prediction in high-dimensional linear models","body":[{"value":"\u003Cp\u003ETITLE: Non-sparse methods for out-of-sample prediction\n       in high-dimensional linear models\n\u003C\/p\u003E\u003Cp\u003ESPEAKER:\u0026nbsp; Dr. Lee Dicker\n\u003C\/p\u003E\u003Cp\u003EABSTRACT:\u003C\/p\u003E\u003Cp\u003EMotivated by questions about dense (non-sparse) signals in\nhigh-dimensional data analysis, we study the unconditional out-of-sample\nprediction error (predictive risk) associated with three classes of dense\nestimators for high-dimensional linear models: Ridge regression\nestimators, scalar multiples of the ordinary least squares estimator\n(which we refer to as James-Stein estimators), and marginal regression\nestimators. Our results require no assumptions about sparsity and imply\nthat in linear models where the number of predictors is roughly\nproportional to the number of observations:\n(i) If the population predictor covariance is known (or if a\nnorm-consistent estimator is available), then the ridge estimator\noutperforms the James-Stein estimator; (ii) both the ridge and James-Stein\nestimators outperform the ordinary least squares estimator, and the\nimprovements offered by these estimators are especially significant when\nthe signal-to-noise ratio is small; and (iii) the marginal estimator has\nserious deficiencies for out-of-sample prediction. We derive new\nclosed-form expressions for the asymptotic predictive risk of the\nestimators, which allow us to precisely quantify the previous claims.\nAdditionally, minimax ridge and James-Stein estimators are identified.\nFinally, we argue that the ridge estimator is, in fact, asymptotically\noptimal among dense estimators for out-of-sample prediction in\nhigh-dimensional linear models.\n\u003C\/p\u003E\u003Cp\u003E\nContact: Lee Dicker \u003Ca href=\u0022mailto:ldicker@stat.rutgers.edu\u0022\u003E\u0026lt;ldicker@stat.rutgers.edu\u0026gt;\u003C\/a\u003E\n\n\u003C\/p\u003E","summary":null,"format":"limited_html"}],"field_subtitle":"","field_summary":"","field_summary_sentence":[{"value":"Non-sparse methods for out-of-sample prediction in high-dimensional linear models"}],"uid":"27187","created_gmt":"2012-01-09 10:12:15","changed_gmt":"2016-10-08 01:56:57","author":"Anita Race","boilerplate_text":"","field_publication":"","field_article_url":"","field_event_time":{"event_time_start":"2012-01-20T11:00:00-05:00","event_time_end":"2012-01-20T12:00:00-05:00","event_time_end_last":"2012-01-20T12:00:00-05:00","gmt_time_start":"2012-01-20 16:00:00","gmt_time_end":"2012-01-20 17:00:00","gmt_time_end_last":"2012-01-20 17:00:00","rrule":null,"timezone":"America\/New_York"},"extras":[],"groups":[{"id":"1242","name":"School of Industrial and Systems Engineering (ISYE)"}],"categories":[],"keywords":[],"core_research_areas":[],"news_room_topics":[],"event_categories":[{"id":"1795","name":"Seminar\/Lecture\/Colloquium"}],"invited_audience":[],"affiliations":[],"classification":[],"areas_of_expertise":[],"news_and_recent_appearances":[],"phone":[],"contact":[{"value":"\u003Cp\u003EMing Yuan\u003C\/p\u003E","format":"limited_html"}],"email":[],"slides":[],"orientation":[],"userdata":""}}}