[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-290454-105":59,"doc-detail-290454-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","model-averaging-and-double-machine-learning-supplementary-tables","Model Averaging and Double Machine Learning - Supplementary tables","","Supplementary material providing simulation results comparing model-averaging and double machine learning (DDML) procedures. Tables A.1–A.3 report mean-squared prediction error, mean bias with standard errors, and average stacking weights. Results are shown for linear and non-linear data-generating processes (DGPs) across different bootstrap sample sizes, nb = 9,915 and nb = 99,150, and for a range of candidate learners and stacking variants based on 1,000 replications.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/model-averaging-and-double-machine-learning-supplementary-tables/290454/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/model-averaging-and-double-machine-learning-supplementary-tables/290454.png","ImageObject",300,407,{"name":92,"@type":93},"Hazel","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-05","2026-09-17",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",12,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What do Tables A.1–A.3 summarize in this supplementary material?","Question",{"text":113,"@type":114},"They summarize simulation performance metrics for candidate learners and stacking approaches, including mean-squared prediction error (Table A.1), mean bias with standard errors (Table A.2), and average stacking weights using OLS as the final learner (Table A.3).","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How are the results organized by data-generating process and bootstrap sample size?",{"text":118,"@type":114},"Table A.1 and A.2 separate results for linear and non-linear DGPs and report outcomes for bootstrap sample sizes nb = 9,915 and nb = 99,150.",{"name":120,"@type":111,"acceptedAnswer":121},"Which learners and stacking approaches are evaluated?",{"text":122,"@type":114},"The tables evaluate OLS, Lasso, Ridge, random forest, gradient boosting, and neural nets, and also compare multiple stacking strategies such as CLS, Average, OLS, Single-best, and pooled and short-stacking variants.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},290454,1789641728,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":140,"language":141,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":67,"update_tm":130,"read_time":145,"preview_page_count":4},137441390410,"https://ap-avatar.wpscdn.com/avatar/2000252f4ab5702993?_k=1776741390130283984","Supplementary material  \nA The benefits of pairing DDML and stacking  \nTable A.1: Mean-squared prediction error  \n\n| Panel (A): Linear DGP | nb = 9 915 |  | nb = 99 150 |  |\n| --- | --- | --- | --- | --- |\n|  | E [Y |X] | E [D|X] | E [Y |X] | E [D|X] |\n| Candidate learners |  |  |  |  |\n| OLS | 3.093 | 0.200 | 3.088 | 0.200 |\n| Lasso with CV (2nd order poly) | 3.095 | 0.200 | 3.088 | 0.200 |\n| Ridge with CV (2nd order poly) | 3.100 | 0.200 | 3.089 | 0.200 |\n| Lasso with CV (10th order poly) | 3.298 | 0.202 | 3.095 | 0.200 |\n| Ridge with CV (10th order poly) | 3.423 | 0.206 | 3.093 | 0.200 |\n| Random forest (low regularization) | 3.613 | 0.233 | 3.698 | 0.239 |\n| Random forest (high regularization) | 3.183 | 0.205 | 3.197 | 0.207 |\n| Gradient boosting (low regularization) | 3.131 | 0.201 | 3.102 | 0.200 |\n| Gradient boosting (high regularization) | 3.151 | 0.201 | 3.137 | 0.201 |\n| Neural net | 3.227 | 0.204 | 3.153 | 0.200 |\n| Panel (B): Non-Linear DGP | E [Y |X] | E [D|X] | E [Y |X] | E [D|X] |\n| Candidate learners |  |  |  |  |\n| OLS | 3.681 | 0.203 | 3.672 | 0.203 |\n| Lasso with CV (2nd order poly) | 3.480 | 0.201 | 3.449 | 0.200 |\n| Ridge with CV (2nd order poly) | 3.479 | 0.201 | 3.449 | 0.200 |\n| Lasso with CV (10th order poly) | 6.161 | 0.223 | 3.422 | 0.200 |\n| Ridge with CV (10th order poly) | 7.431 | 0.230 | 3.424 | 0.200 |\n| Random forest (low regularization) | 3.789 | 0.231 | 3.515 | 0.236 |\n| Random forest (high regularization) | 3.588 | 0.204 | 3.251 | 0.205 |\n| Gradient boosting (low regularization) | 3.345 | 0.200 | 3.095 | 0.198 |\n| Gradient boosting (high regularization) | 3.399 | 0.200 | 3.216 | 0.199 |\n| Neural net | 3.694 | 0.205 | 3.510 | 0.200 |\n\nNotes: The table shows the mean-squared prediction error of each candidate learner from the simulation example in Section 4.1 . The bootstrap sample size is n b = 9 915 or 99 150. Results are based on 1 000 replications. See Table 1 for more information.  \nTable A.2: Bias in the Linear and Non-Linear DGP  \n\n|  | Panel (A): Linear DGP\u003Cbr>nb = 9 915 99 150\u003Cbr>Bias s.e. Bias s.e. | Panel (B): Non-linear DGP |\n| --- | --- | --- |\n|  |  | nb = 9 915 99 150\u003Cbr>Bias s.e. Bias s.e. |\n| Full sample: |  |  |\n| OLS | 49.9 39.6 -6.8 12.6 | -2588.9 46.5 -2632.3 14.8 |\n| PDS-Lasso | 48.4 39.6 -4.2 12.6 | -2598.7 46.5 -2631.6 14.8 |\n| DDML methods: |  |  |\n| Candidate learners |  |  |\n| OLS | 46.2 39.7 -6.9 12.6 | -2613.0 47.5 -2635.4 14.8 |\n| Lasso with CV (2nd order poly) | 50.9 39.7 -6.2 12.6 | 703.7 44.5 718.5 13.5 |\n| Ridge with CV (2nd order poly) | 48.2 39.9 -6.9 12.6 | 767.4 44.6 729.3 13.5 |\n| Lasso with CV (10th order poly) | 248.1 266.6 55.9 12.6 | -4109.0 1325.8 7.4 22.5 |\n| Ridge with CV (10th order poly) | 1230.1 401.8 31.6 12.6 | -5126.2 1713.9 9.6 23.3 |\n| Random forest (low regularization) | -74.7 48.6 -25.2 16.0 | -96.1 48.5 -37.5 15.4 |\n| Random forest (high regularization) | 69.1 41.7 -23.5 13.2 | -159.7 43.5 -4.2 13.0 |\n| Gradient boosting (low regularization) | 12.1 40.1 -24.2 12.6 | 8.5 42.7 30.9 12.4 |\n| Gradient boosting (high regularization) | 114.8 39.8 66.9 12.5 | 162.0 42.1 200.1 12.6 |\n| Neural net | 394.2 43.1 9.1 13.6 | -601.3 46.5 -131.9 14.3 |\n| Stacking approaches |  |  |\n| Stacking: CLS | 42.8 40.2 -7.5 12.6 | 133.9 195.6 37.8 12.4 |\n| Stacking: Average | 107.7 51.2 -6.5 12.6 | 94.0 110.3 72.3 12.7 |\n| Stacking: OLS | -129.3 96.2 -9.4 14.9 | -204.8 405.2 17.5 17.8 |\n| Stacking: Single-best | 43.7 39.9 -8.6 12.6 | -121.9 272.9 30.9 12.4 |\n| Short-stacking: CLS | 45.0 39.7 -7.0 12.6 | 162.7 42.0 33.6 12.4 |\n| Short-stacking: Average | 107.7 51.2 -6.5 12.6 | 94.0 110.3 72.3 12.7 |\n| Short-stacking: OLS | 37.6 39.6 -7.8 12.6 | 123.6 41.7 29.5 12.3 |\n| Short-stacking: Single-best | 44.4 39.7 -8.3 12.6 | 71.7 42.6 30.9 12.4 |\n| Pooled stacking: CLS | 58.6 41.4 -7.1 12.6 | 209.8 63.7 37.5 12.4 |\n| Pooled stacking: Average | 107.7 51.2 -6.5 12.6 | 94.0 110.3 72.3 12.7 |\n| Pooled stacking: OLS | 46.5 47.8 -7.8 12.6 | 234.5 124.9 30.6 12.3 |\n| Pooled ","cbCaitVP3ddMiLu8","https://ap.wps.com/l/cbCaitVP3ddMiLu8","pdf",781553,14,"English","# Supplementary material\n## Benefits of pairing DDML and stacking\n## Table A.1: Mean-squared prediction error\n## Table A.2: Bias in the Linear and Non-Linear DGP\n## Table A.3: Average stacking weights using OLS as the final learner","[{\"question\":\"What do Tables A.1–A.3 summarize in this supplementary material?\",\"answer\":\"They summarize simulation performance metrics for candidate learners and stacking approaches, including mean-squared prediction error (Table A.1), mean bias with standard errors (Table A.2), and average stacking weights using OLS as the final learner (Table A.3).\"},{\"question\":\"How are the results organized by data-generating process and bootstrap sample size?\",\"answer\":\"Table A.1 and A.2 separate results for linear and non-linear DGPs and report outcomes for bootstrap sample sizes nb = 9,915 and nb = 99,150.\"},{\"question\":\"Which learners and stacking approaches are evaluated?\",\"answer\":\"The tables evaluate OLS, Lasso, Ridge, random forest, gradient boosting, and neural nets, and also compare multiple stacking strategies such as CLS, Average, OLS, Single-best, and pooled and short-stacking variants.\"}]","Model Averaging and Double Machine Learning - Supplementary tables | PDF",35]