{"id":"https://openalex.org/W1989738929","doi":"https://doi.org/10.1198/004017004000000149","title":"The Local Piecewisely Linear Kernel Smoothing Procedure for Fitting Jump Regression Surfaces","display_name":"The Local Piecewisely Linear Kernel Smoothing Procedure for Fitting Jump Regression Surfaces","publication_year":2004,"publication_date":"2004-02-01","ids":{"openalex":"https://openalex.org/W1989738929","doi":"https://doi.org/10.1198/004017004000000149","mag":"1989738929"},"language":"en","primary_location":{"id":"doi:10.1198/004017004000000149","is_oa":false,"landing_page_url":"https://doi.org/10.1198/004017004000000149","pdf_url":null,"source":{"id":"https://openalex.org/S985303","display_name":"Technometrics","issn_l":"0040-1706","issn":["0040-1706","1537-2723"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Technometrics","raw_type":"journal-article"},"type":"article","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/A5058863622","display_name":"Peihua Qiu","orcid":"https://orcid.org/0000-0003-4439-9466"},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Peihua Qiu","raw_affiliation_strings":["School of Statistics, University of Minnesota, Minneapolis, MN 55455","University of\u00a0Minnesota"],"affiliations":[{"raw_affiliation_string":"School of Statistics, University of Minnesota, Minneapolis, MN 55455","institution_ids":["https://openalex.org/I130238516"]},{"raw_affiliation_string":"University of\u00a0Minnesota","institution_ids":["https://openalex.org/I130238516"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5058863622"],"corresponding_institution_ids":["https://openalex.org/I130238516"],"apc_list":null,"apc_paid":null,"fwci":1.9311,"has_fulltext":false,"cited_by_count":35,"citation_normalized_percentile":{"value":0.86568458,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"46","issue":"1","first_page":"87","last_page":"98"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12549","display_name":"Image and Object Detection Techniques","score":0.9912999868392944,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12549","display_name":"Image and Object Detection Techniques","score":0.9912999868392944,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10770","display_name":"Soil Geostatistics and Mapping","score":0.9911999702453613,"subfield":{"id":"https://openalex.org/subfields/2305","display_name":"Environmental Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10894","display_name":"Groundwater flow and contamination studies","score":0.9761999845504761,"subfield":{"id":"https://openalex.org/subfields/2305","display_name":"Environmental Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.8731385469436646},{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.7821424007415771},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7689421772956848},{"id":"https://openalex.org/keywords/jump","display_name":"Jump","score":0.6511570811271667},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.5127013921737671},{"id":"https://openalex.org/keywords/kernel-density-estimation","display_name":"Kernel density estimation","score":0.47555822134017944},{"id":"https://openalex.org/keywords/kernel-smoother","display_name":"Kernel smoother","score":0.46047157049179077},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.4520083963871002},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.4245993196964264},{"id":"https://openalex.org/keywords/bivariate-analysis","display_name":"Bivariate analysis","score":0.42445510625839233},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4218946397304535},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.41127872467041016},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.3206295371055603},{"id":"https://openalex.org/keywords/kernel-method","display_name":"Kernel method","score":0.3002185821533203},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.21255970001220703},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16208359599113464},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10807457566261292},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.06853562593460083},{"id":"https://openalex.org/keywords/support-vector-machine","display_name":"Support vector machine","score":0.06748142838478088}],"concepts":[{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.8731385469436646},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.7821424007415771},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7689421772956848},{"id":"https://openalex.org/C2780695682","wikidata":"https://www.wikidata.org/wiki/Q4005959","display_name":"Jump","level":2,"score":0.6511570811271667},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.5127013921737671},{"id":"https://openalex.org/C71134354","wikidata":"https://www.wikidata.org/wiki/Q458825","display_name":"Kernel density estimation","level":3,"score":0.47555822134017944},{"id":"https://openalex.org/C27406209","wikidata":"https://www.wikidata.org/wiki/Q6394203","display_name":"Kernel smoother","level":5,"score":0.46047157049179077},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.4520083963871002},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.4245993196964264},{"id":"https://openalex.org/C64341305","wikidata":"https://www.wikidata.org/wiki/Q4919225","display_name":"Bivariate analysis","level":2,"score":0.42445510625839233},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4218946397304535},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.41127872467041016},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3206295371055603},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.3002185821533203},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.21255970001220703},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16208359599113464},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10807457566261292},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.06853562593460083},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.06748142838478088},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C75866337","wikidata":"https://www.wikidata.org/wiki/Q7280263","display_name":"Radial basis function kernel","level":4,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1198/004017004000000149","is_oa":false,"landing_page_url":"https://doi.org/10.1198/004017004000000149","pdf_url":null,"source":{"id":"https://openalex.org/S985303","display_name":"Technometrics","issn_l":"0040-1706","issn":["0040-1706","1537-2723"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Technometrics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.75.5904","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.75.5904","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.stat.umn.edu/~qiu/research/preserve1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.76.5399","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.76.5399","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.stat.umn.edu/~qiu/research/preserve1.ps","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Life below water","id":"https://metadata.un.org/sdg/14","score":0.8600000143051147}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W1495241956","https://openalex.org/W1507028917","https://openalex.org/W1544729927","https://openalex.org/W1554544485","https://openalex.org/W1597926580","https://openalex.org/W1971281902","https://openalex.org/W1975285668","https://openalex.org/W1981352825","https://openalex.org/W1983649039","https://openalex.org/W1984462891","https://openalex.org/W1988684120","https://openalex.org/W1989457171","https://openalex.org/W1992643144","https://openalex.org/W1996705486","https://openalex.org/W1996887624","https://openalex.org/W2013378870","https://openalex.org/W2020999234","https://openalex.org/W2024081693","https://openalex.org/W2031314447","https://openalex.org/W2050024377","https://openalex.org/W2051195364","https://openalex.org/W2069322137","https://openalex.org/W2069888879","https://openalex.org/W2087373255","https://openalex.org/W2095447539","https://openalex.org/W2096299256","https://openalex.org/W2102716230","https://openalex.org/W2105892412","https://openalex.org/W2114289522","https://openalex.org/W2131142116","https://openalex.org/W2144400918","https://openalex.org/W2154065388","https://openalex.org/W2158940042","https://openalex.org/W2163591144","https://openalex.org/W2319794630","https://openalex.org/W2330147958","https://openalex.org/W2786093300","https://openalex.org/W3021510377","https://openalex.org/W4211255756","https://openalex.org/W4230966727","https://openalex.org/W4236407158","https://openalex.org/W4240461561","https://openalex.org/W4253016408"],"related_works":["https://openalex.org/W2920855166","https://openalex.org/W4205267905","https://openalex.org/W3142731338","https://openalex.org/W3149448578","https://openalex.org/W1602884087","https://openalex.org/W2222544391","https://openalex.org/W2244226369","https://openalex.org/W2764059675","https://openalex.org/W2554628716","https://openalex.org/W3148067335"],"abstract_inverted_index":{"It":[0,223],"is":[1,12,70,110,119,131,144,153,189,215],"known":[2],"that":[3,37,129],"a":[4,28,59,62,65,113,122,155],"surface":[5,43,89,127,168,194,206,235,240,246],"fitted":[6,71,82],"by":[7,134],"conventional":[8,32,202],"local":[9,33,50],"smoothing":[10,34,53],"procedures":[11,35,40],"not":[13],"statistically":[14],"consistent":[15],"at":[16,90,128,159,196],"the":[17,21,38,42,49,76,88,91,100,104,107,116,126,135,138,142,147,150,163,167,176,183,186,193,197,204],"jump":[18,156,234],"locations":[19],"of":[20,61,78,87,137,162,180,182],"true":[22],"regression":[23],"surface.":[24],"This":[25],"article":[26],"suggests":[27],"procedure":[29,54],"for":[30],"modifying":[31],"such":[36],"modified":[39],"fit":[41],"with":[44,72],"jumps":[45,74],"preserved":[46],"automatically.":[47],"Taking":[48],"linear":[51,68],"kernel":[52],"as":[55],"an":[56,209],"example,":[57],"in":[58,99,242,248],"neighborhood":[60],"given":[63,92,117,151,198],"point,":[64,93,124,157],"bivariate":[66],"piecewisely":[67],"function":[69,83],"possible":[73],"along":[75],"boundaries":[77],"four":[79,85,101,108,139,164,184],"quadrants.":[80,102],"The":[81],"provides":[84],"estimators":[86,109,165],"which":[94],"are":[95],"constructed":[96],"from":[97],"observations":[98],"When":[103,141],"difference":[105,143],"among":[106],"smaller":[111],"than":[112,146],"threshold":[114,148],"value,":[115,149],"point":[118,130,152],"most":[120,201],"likely":[121,154],"continuous":[123],"and":[125,158,213,219,232,244,250],"then":[132],"estimated":[133],"average":[136],"estimators.":[140],"larger":[145],"least":[160],"one":[161,188],"estimates":[166],"well":[169],"under":[170],"some":[171],"regularity":[172],"conditions.":[173],"By":[174],"comparing":[175],"weighted":[177],"residual":[178],"sums":[179],"squares":[181],"estimators,":[185,203],"best":[187],"selected":[190],"to":[191,217,221,228],"define":[192],"estimator":[195,207],"point.":[199],"Like":[200],"current":[205],"has":[208],"explicit":[210],"mathematical":[211],"formula":[212],"thus":[214],"easy":[216],"compute":[218],"convenient":[220],"use.":[222],"can":[224],"be":[225],"applied":[226],"directly":[227],"image":[229],"reconstruction":[230],"problems":[231],"other":[233],"estimation":[236,241,247],"problems,":[237],"including":[238],"mine":[239],"geology":[243],"equitemperature":[245],"meteorology":[249],"oceanography.":[251]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}