{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T15:22:44Z","timestamp":1762010564092,"version":"build-2065373602"},"reference-count":43,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[1995,9,1]],"date-time":"1995-09-01T00:00:00Z","timestamp":809913600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[1995,9,1]]},"abstract":"<jats:title>SUMMARY<\/jats:title>\n               <jats:p>A new theoretical point of view is discussed in the framework of density estimation. The multivariate true density, viewed as a prior or penalizing factor in a Bayesian framework, is modelled by a Gibbs potential. Estimating the density consists in maximizing the posterior. For efficiency of time, we are interested in an approximate estimator f\u0302 = B\u03c0 of the true density f, where B is a stochastic operator and \u03c0 is the raw histogram. Then, we investigate the discrimination problem, introducing an adaptive bandwidth depending on the k nearest neighbours and chosen to optimize the cross-validation criterion. Our final classification algorithm referred to as APML for approximate penalized maximum likelihood compares favourably in terms of error rate and time efficiency with other algorithms tested, including multinormal, nearest neighbour and convex hull classifiers.<\/jats:p>","DOI":"10.1111\/j.2517-6161.1995.tb02044.x","type":"journal-article","created":{"date-parts":[[2018,12,7]],"date-time":"2018-12-07T06:28:20Z","timestamp":1544164100000},"page":"501-517","source":"Crossref","is-referenced-by-count":8,"title":["Multivariate Discriminant Analysis and Maximum Penalized Likelihood Density Estimation"],"prefix":"10.1093","volume":"57","author":[{"given":"Vincent","family":"Granville","sequence":"first","affiliation":[{"name":"Facult\u00e9s Universitaires de Namur \u00a0 Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jean Paul","family":"Rasson","sequence":"additional","affiliation":[{"name":"Facult\u00e9s Universitaires de Namur \u00a0 Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2018,12,5]]},"reference":[{"key":"2024090921150729100_rssb02044-cit-0001","first-page":"157","article-title":"Errors in binary images and an Lp version of the Hausdorff metric","volume":"10","author":"Baddeley","year":"1992","journal-title":"Nieuw Arch. 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