H T Banks, K B Flores, I G Rosen, E M Rutter, Melike Sirlanci, W Clayton Thompson
{"title":"THE PROHOROV METRIC FRAMEWORK AND AGGREGATE DATA INVERSE PROBLEMS FOR RANDOM PDEs.","authors":"H T Banks, K B Flores, I G Rosen, E M Rutter, Melike Sirlanci, W Clayton Thompson","doi":"","DOIUrl":null,"url":null,"abstract":"<p><p>We consider nonparametric estimation of probability measures for parameters in problems where only aggregate (population level) data are available. We summarize an existing computational method for the estimation problem which has been developed over the past several decades [24, 5, 12, 28, 16]. Theoretical results are presented which establish the existence and consistency of very general (ordinary, generalized and other) least squares estimates and estimators for the measure estimation problem with specific application to random PDEs.</p>","PeriodicalId":92887,"journal":{"name":"Communications in applied analysis","volume":"22 3","pages":"415-446"},"PeriodicalIF":0.0000,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9365078/pdf/nihms-1826881.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in applied analysis","FirstCategoryId":"1085","ListUrlMain":"","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2018/6/19 0:00:00","PubModel":"Epub","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
We consider nonparametric estimation of probability measures for parameters in problems where only aggregate (population level) data are available. We summarize an existing computational method for the estimation problem which has been developed over the past several decades [24, 5, 12, 28, 16]. Theoretical results are presented which establish the existence and consistency of very general (ordinary, generalized and other) least squares estimates and estimators for the measure estimation problem with specific application to random PDEs.
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