{"id":"https://openalex.org/W57041892","doi":"https://doi.org/10.1007/978-3-642-57489-4_79","title":"Robust Principal Components Regression","display_name":"Robust Principal Components Regression","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W57041892","doi":"https://doi.org/10.1007/978-3-642-57489-4_79","mag":"57041892"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-642-57489-4_79","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-57489-4_79","pdf_url":null,"source":{"id":"https://openalex.org/S4306506691","display_name":"COMPSTAT","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Compstat","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017966168","display_name":"Sabine Verboven","orcid":null},"institutions":[{"id":"https://openalex.org/I149213910","display_name":"University of Antwerp","ror":"https://ror.org/008x57b05","country_code":"BE","type":"education","lineage":["https://openalex.org/I149213910"]}],"countries":["BE"],"is_corresponding":true,"raw_author_name":"Sabine Verboven","raw_affiliation_strings":["Department of Mathematics and Computer Science, University of Antwerp, Universiteitsplein 1, Wilrijk, Belgium, 2160"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, University of Antwerp, Universiteitsplein 1, Wilrijk, Belgium, 2160","institution_ids":["https://openalex.org/I149213910"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080298759","display_name":"Mia Hubert","orcid":"https://orcid.org/0000-0001-6398-4850"},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Mia Hubert","raw_affiliation_strings":["Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200B, B-3001, Heverlee, Belgium"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200B, B-3001, Heverlee, Belgium","institution_ids":["https://openalex.org/I99464096"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5017966168"],"corresponding_institution_ids":["https://openalex.org/I149213910"],"apc_list":null,"apc_paid":null,"fwci":2.1494,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.85438144,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"515","last_page":"520"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11871","display_name":"Advanced Statistical Methods and Models","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11871","display_name":"Advanced Statistical Methods and Models","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10640","display_name":"Spectroscopy and Chemometric Analyses","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/1602","display_name":"Analytical Chemistry"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11443","display_name":"Advanced Statistical Process Monitoring","score":0.9379000067710876,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/multicollinearity","display_name":"Multicollinearity","score":0.7456285357475281},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6973696351051331},{"id":"https://openalex.org/keywords/principal-component-analysis","display_name":"Principal component analysis","score":0.6839936375617981},{"id":"https://openalex.org/keywords/outlier","display_name":"Outlier","score":0.6103715896606445},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.6028050780296326},{"id":"https://openalex.org/keywords/principal-component-regression","display_name":"Principal component regression","score":0.5599509477615356},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.5484774708747864},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.5321784615516663},{"id":"https://openalex.org/keywords/robust-regression","display_name":"Robust regression","score":0.5277113318443298},{"id":"https://openalex.org/keywords/data-matrix","display_name":"Data Matrix","score":0.5119979977607727},{"id":"https://openalex.org/keywords/design-matrix","display_name":"Design matrix","score":0.5113679766654968},{"id":"https://openalex.org/keywords/covariance-matrix","display_name":"Covariance matrix","score":0.4907006025314331},{"id":"https://openalex.org/keywords/partial-least-squares-regression","display_name":"Partial least squares regression","score":0.4758434295654297},{"id":"https://openalex.org/keywords/collinearity","display_name":"Collinearity","score":0.4754364490509033},{"id":"https://openalex.org/keywords/linear-regression","display_name":"Linear regression","score":0.4630439877510071},{"id":"https://openalex.org/keywords/variance-inflation-factor","display_name":"Variance inflation factor","score":0.4535147547721863},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.4507017135620117},{"id":"https://openalex.org/keywords/least-trimmed-squares","display_name":"Least trimmed squares","score":0.4385640025138855},{"id":"https://openalex.org/keywords/regression-analysis","display_name":"Regression analysis","score":0.4243243932723999},{"id":"https://openalex.org/keywords/generalized-least-squares","display_name":"Generalized least squares","score":0.2721450924873352}],"concepts":[{"id":"https://openalex.org/C189285262","wikidata":"https://www.wikidata.org/wiki/Q1332350","display_name":"Multicollinearity","level":3,"score":0.7456285357475281},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6973696351051331},{"id":"https://openalex.org/C27438332","wikidata":"https://www.wikidata.org/wiki/Q2873","display_name":"Principal component analysis","level":2,"score":0.6839936375617981},{"id":"https://openalex.org/C79337645","wikidata":"https://www.wikidata.org/wiki/Q779824","display_name":"Outlier","level":2,"score":0.6103715896606445},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6028050780296326},{"id":"https://openalex.org/C74887250","wikidata":"https://www.wikidata.org/wiki/Q3455892","display_name":"Principal component regression","level":3,"score":0.5599509477615356},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.5484774708747864},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.5321784615516663},{"id":"https://openalex.org/C70259352","wikidata":"https://www.wikidata.org/wiki/Q1847839","display_name":"Robust regression","level":3,"score":0.5277113318443298},{"id":"https://openalex.org/C2780985081","wikidata":"https://www.wikidata.org/wiki/Q676502","display_name":"Data Matrix","level":5,"score":0.5119979977607727},{"id":"https://openalex.org/C203233044","wikidata":"https://www.wikidata.org/wiki/Q5264358","display_name":"Design matrix","level":3,"score":0.5113679766654968},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.4907006025314331},{"id":"https://openalex.org/C22354355","wikidata":"https://www.wikidata.org/wiki/Q422009","display_name":"Partial least squares regression","level":2,"score":0.4758434295654297},{"id":"https://openalex.org/C106192678","wikidata":"https://www.wikidata.org/wiki/Q1419761","display_name":"Collinearity","level":2,"score":0.4754364490509033},{"id":"https://openalex.org/C48921125","wikidata":"https://www.wikidata.org/wiki/Q10861030","display_name":"Linear regression","level":2,"score":0.4630439877510071},{"id":"https://openalex.org/C152732102","wikidata":"https://www.wikidata.org/wiki/Q13434396","display_name":"Variance inflation factor","level":4,"score":0.4535147547721863},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.4507017135620117},{"id":"https://openalex.org/C25294789","wikidata":"https://www.wikidata.org/wiki/Q6510410","display_name":"Least trimmed squares","level":4,"score":0.4385640025138855},{"id":"https://openalex.org/C152877465","wikidata":"https://www.wikidata.org/wiki/Q208042","display_name":"Regression analysis","level":2,"score":0.4243243932723999},{"id":"https://openalex.org/C188649462","wikidata":"https://www.wikidata.org/wiki/Q2246261","display_name":"Generalized least squares","level":3,"score":0.2721450924873352},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C44465124","wikidata":"https://www.wikidata.org/wiki/Q713623","display_name":"Clade","level":4,"score":0.0},{"id":"https://openalex.org/C193252679","wikidata":"https://www.wikidata.org/wiki/Q242125","display_name":"Phylogenetic tree","level":3,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-642-57489-4_79","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-57489-4_79","pdf_url":null,"source":{"id":"https://openalex.org/S4306506691","display_name":"COMPSTAT","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Compstat","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W635284460","https://openalex.org/W1594738692","https://openalex.org/W1969428313","https://openalex.org/W1979486458","https://openalex.org/W1980262437","https://openalex.org/W2010074546","https://openalex.org/W2010951077","https://openalex.org/W2054834816","https://openalex.org/W2081862629","https://openalex.org/W2089052299","https://openalex.org/W2112440119","https://openalex.org/W2129249398","https://openalex.org/W2152701363","https://openalex.org/W2498631646","https://openalex.org/W4233774682","https://openalex.org/W4243563432"],"related_works":["https://openalex.org/W2152475145","https://openalex.org/W2076812056","https://openalex.org/W2086982132","https://openalex.org/W1923984923","https://openalex.org/W3122671039","https://openalex.org/W3124749190","https://openalex.org/W2960901905","https://openalex.org/W2511760895","https://openalex.org/W4231620018","https://openalex.org/W4238098653"],"abstract_inverted_index":{"We":[0,173,210],"consider":[1],"the":[2,23,32,38,54,64,79,125,131,134,139,151,166,171,196,213,221,231,246,249,258,275,279],"multivariate":[3,222],"linear":[4],"regression":[5,101,179],"model":[6],"with":[7,41],"p":[8,75],"explanatory":[9,120],"variables":[10,17,143,215],"X":[11,80,82],"and":[12,109,199,272],"q":[13],"\u2265":[14],"1":[15],"response":[16,142,214],"Y.":[18],"Moreover":[19,68,261],"we":[20,235,262],"assume":[21],"that":[22,43,53],"regressors":[24,219],"are":[25,44,123,144,161],"multicollinear.":[26],"This":[27],"situation":[28],"often":[29],"occurs":[30],"in":[31,63,170,278],"calibration":[33],"of":[34,66,118,133,138,158,168,184,206,233,248,252],"chemometrical":[35],"data,":[36],"where":[37],"X-variables":[39,197],"correspond":[40,129],"spectra":[42],"measured":[45],"at":[46],"many":[47,88],"frequencies.":[48],"It":[49,241],"is":[50,98,105,193,242,255],"well":[51],"known":[52],"classical":[55],"least":[56,153],"squares":[57,154],"estimator":[58],"has":[59],"a":[60,115,175,188,203,237],"large":[61],"variance":[62,251],"presence":[65,167],"multicollinearity.":[67],"it":[69,104],"can":[70],"not":[71],"be":[72],"computed":[73],"when":[74],">":[76],"n":[77],"since":[78,103],"t":[81],"matrix":[83,137],"then":[84,145,211],"becomes":[85],"singular.":[86],"Therefore":[87],"biased":[89],"estimators":[90],"have":[91],"been":[92],"proposed.":[93],"A":[94],"very":[95,163],"appealing":[96],"method":[97,180,224],"principal":[99,126,177,190],"components":[100,149,178,191],"(PCR)":[102],"easy":[106],"to":[107,110,130,165,195,270,273],"understand":[108],"compute.":[111],"PCR":[112],"first":[113],"constructs":[114],"new":[116],"set":[117,205],"uncorrelated":[119],"variables,":[121],"which":[122,181,254,267],"called":[124],"components.":[127],"They":[128],"eigenvectors":[132],"sample":[135],"covariance":[136],"X-variables.":[140],"The":[141],"regressed":[146],"on":[147,217],"these":[148,218],"using":[150,220],"(multivariate)":[152],"estimator.":[155],"Both":[156],"stages":[157],"this":[159],"procedure":[160],"however":[162],"sensitive":[164],"outliers":[169,277],"data.":[172,280],"present":[174],"robust":[176,189,238,250,259],"also":[182],"consists":[183],"two":[185],"steps.":[186],"First":[187],"analysis":[192],"applied":[194],"(Hubert":[198],"Rousseeuw,":[200],"2002),":[201],"yielding":[202],"smaller":[204],"k":[207],"orthogonal":[208],"regressors.":[209],"regress":[212],"Y":[216,253],"MCD-regression":[223],"(Rousseeuw":[225],"et":[226],"al.":[227],"2000).":[228],"To":[229],"select":[230],"number":[232],"regressors,":[234],"propose":[236,263],"R":[239],"2.":[240],"roughly":[243],"defined":[244],"as":[245],"proportion":[247],"explained":[256],"by":[257],"fit.":[260],"several":[264],"diagnostic":[265],"plots,":[266],"allow":[268],"us":[269],"visualize":[271],"distinguish":[274],"possible":[276]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}