{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:36:56Z","timestamp":1760243816434,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2011,6,23]],"date-time":"2011-06-23T00:00:00Z","timestamp":1308787200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Peelle\u2019s Pertinent Puzzle (PPP) was described in 1987 in the context of estimating fundamental parameters that arise in nuclear interaction experiments. In PPP, generalized least squares (GLS) parameter estimates fell outside the range of the data, which has raised concerns that GLS is somehow flawed and has led to suggested alternatives to GLS estimators. However, there have been no corresponding performance comparisons among methods, and one suggested approach involving simulated data realizations is statistically incomplete. Here we provide performance comparisons among estimators, introduce approximate Bayesian computation (ABC) using density estimation applied to simulated data realizations to produce an alternative to the incomplete approach, complete the incompletely specified approach, and show that estimation error in the assumed covariance matrix cannot always be ignored.<\/jats:p>","DOI":"10.3390\/a4020115","type":"journal-article","created":{"date-parts":[[2011,6,24]],"date-time":"2011-06-24T08:19:30Z","timestamp":1308903570000},"page":"115-130","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Alternatives to the Least Squares Solution to Peelle\u2019s Pertinent Puzzle"],"prefix":"10.3390","volume":"4","author":[{"given":"Tom","family":"Burr","sequence":"first","affiliation":[{"name":"Statistical Sciences, Los Alamos National Laboratory, Los Alamos, NM 87545, USA"}]},{"given":"Todd","family":"Graves","sequence":"additional","affiliation":[{"name":"Statistical Sciences, Los Alamos National Laboratory, Los Alamos, NM 87545, USA"}]},{"given":"Nicolas","family":"Hengartner","sequence":"additional","affiliation":[{"name":"Information Sciences, Los Alamos National Laboratory, Los Alamos, NM 87545, USA"}]},{"given":"Toshihiko","family":"Kawano","sequence":"additional","affiliation":[{"name":"Nuclear and Particle Physics, Los Alamos National Laboratory, Los Alamos, NM 87545, USA"}]},{"given":"Feng","family":"Pan","sequence":"additional","affiliation":[{"name":"Decision Applications, Los Alamos National Laboratory, Los Alamos, NM 87545, USA"}]},{"given":"Patrick","family":"Talou","sequence":"additional","affiliation":[{"name":"Nuclear and Particle Physics, Los Alamos National Laboratory, Los Alamos, NM 87545, USA"}]}],"member":"1968","published-online":{"date-parts":[[2011,6,23]]},"reference":[{"key":"ref_1","unstructured":"Peelle, R. 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Assoc."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Hastie, T., Tibshirani, R., and Friedman, J. (2001). The Elements of Statistical Learning, Springer.","DOI":"10.1007\/978-0-387-21606-5"}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/4\/2\/115\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:56:31Z","timestamp":1760219791000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/4\/2\/115"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,6,23]]},"references-count":25,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2011,6]]}},"alternative-id":["a4020115"],"URL":"https:\/\/doi.org\/10.3390\/a4020115","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2011,6,23]]}}}