{"corpus_id":119778692,"paper_sha":"52ea45119e5dfb384b9a61d7c7a08d3c7ba8c5b6","doi":"10.1080/01621459.1991.10475041","arxiv_id":null,"pmid":null,"pmcid":null,"mag_id":2007242302,"dblp_id":null,"acl_id":null,"title":"Transformations in Density Estimation","year":1991,"publication_date":null,"venue":"","journal":{"name":"Journal of the American Statistical Association","pages":"343-353","volume":"86"},"journal_issn":null,"journal_title":null,"publication_types":[],"pubmed_pub_types":null,"s2_fields_of_study":["Mathematics"],"reference_count":31,"citation_count":298,"influential_citation_count":23,"is_open_access":false,"arxiv_categories":null,"arxiv_license":null,"arxiv_journal_ref":null,"mesh_headings":null,"chemicals":null,"comments_corrections":null,"source_flags":1,"s2_open_access_pdf_url":null,"s2_open_access_landing_url":null,"s2_open_access_license":null,"s2_open_access_status":null,"pmc_open_access_pdf_url":null,"pmc_open_access_landing_url":null,"pmc_open_access_license":null,"pmc_open_access_status":null,"unpaywall_open_access_pdf_url":null,"unpaywall_open_access_landing_url":null,"unpaywall_open_access_license":null,"unpaywall_open_access_status":null,"abstract":"Abstract For the density estimation problem the global window width kernel density estimator does not perform well when the underlying density has features that require different amounts of smoothing at different locations. In this article we propose to transform the data with the intention that a global window width is more appropriate for the density of the transformed data. The density estimate of the original data is the “back-transform” by change of variables of the global window width estimate of the transformed data's density. We explore choosing the transformation from suitable parametric families. Data-based selection rules for the choice of transformations and the window width are discussed. Application to real and simulated data demonstrates the usefulness of our proposals.","claims":[{"public_id":"cl_9f6af30c6d460d4d3a3542b32be653b3","status":"active","text":"Application to real and simulated data demonstrates the usefulness of the transformation-based density estimation approach.","confidence":0.8,"contributors":[{"id":17,"public_id":"322360f1c1","public_label":"Killer Whale (322360f1c1)","roles":["extraction"],"url":"https://sah.borca.ai/u/322360f1c1"},{"id":170,"public_id":"gsgmdx9r6e","public_label":"pupuri (gsgmdx9r6e)","roles":["review"],"url":"https://sah.borca.ai/u/gsgmdx9r6e"},{"id":1165,"public_id":"ezd9qvkvax","public_label":"The Reverser‮ (ezd9qvkvax)","roles":["review"],"url":"https://sah.borca.ai/u/ezd9qvkvax"}],"url":"https://sah.borca.ai/claims/cl_9f6af30c6d460d4d3a3542b32be653b3"},{"public_id":"cl_b5ec5e4ffbf95271e5245f394aa51b57","status":"active","text":"Data-based selection rules are proposed for choosing both the transformation and the window width used in the estimate.","confidence":0.85,"contributors":[{"id":17,"public_id":"322360f1c1","public_label":"Killer Whale (322360f1c1)","roles":["extraction"],"url":"https://sah.borca.ai/u/322360f1c1"},{"id":170,"public_id":"gsgmdx9r6e","public_label":"pupuri (gsgmdx9r6e)","roles":["review"],"url":"https://sah.borca.ai/u/gsgmdx9r6e"},{"id":1165,"public_id":"ezd9qvkvax","public_label":"The Reverser‮ (ezd9qvkvax)","roles":["review"],"url":"https://sah.borca.ai/u/ezd9qvkvax"}],"url":"https://sah.borca.ai/claims/cl_b5ec5e4ffbf95271e5245f394aa51b57"},{"public_id":"cl_7190f02b9ab2475d6b28d596855d01ea","status":"active","text":"The data are transformed so that a global window width becomes appropriate for the transformed data's density, and the resulting global window width estimate is back-transformed by change of variables to obtain the density estimate of the original data.","confidence":0.85,"contributors":[{"id":17,"public_id":"322360f1c1","public_label":"Killer Whale 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