{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,18]],"date-time":"2025-12-18T14:15:04Z","timestamp":1766067304293},"reference-count":18,"publisher":"Walter de Gruyter GmbH","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021,6,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The intersection or the overlap region of two <jats:italic>n<\/jats:italic>-dimensional ellipsoids plays an important role in statistical decision making in a number of applications. For instance, the intersection volume of two <jats:italic>n<\/jats:italic>-dimensional ellipsoids has been employed to define dissimilarity measures in time series clustering (see [M. Bakoben, T. Bellotti and N. M. Adams,\nImproving clustering performance by incorporating uncertainty,\nPattern Recognit. Lett. 77 2016, 28\u201334]). Formulas for the intersection volumes of two <jats:italic>n<\/jats:italic>-dimensional ellipsoids are not known. In this article, we first derive exact formulas to determine the intersection volume of two hyper-ellipsoids satisfying a certain condition. Then we adapt and extend two geometric type Monte Carlo methods that in principle allow us\nto compute the intersection volume of any two generalized convex\nhyper-ellipsoids. Using the exact formulas, we evaluate the performance of\nthe two Monte Carlo methods. Our numerical experiments show that\nsufficiently accurate estimates can be obtained for a reasonably wide range\nof <jats:italic>n<\/jats:italic>, and that the sample-mean method is more efficient. Finally, we develop an elementary fast Monte Carlo method to determine,\nwith high probability, if two <jats:italic>n<\/jats:italic>-ellipsoids are separated or overlap.<\/jats:p>","DOI":"10.1515\/mcma-2021-2087","type":"journal-article","created":{"date-parts":[[2021,4,29]],"date-time":"2021-04-29T21:42:39Z","timestamp":1619732559000},"page":"153-167","source":"Crossref","is-referenced-by-count":4,"title":["On intersection volumes of confidence hyper-ellipsoids and two geometric Monte Carlo methods"],"prefix":"10.1515","volume":"27","author":[{"given":"Nima","family":"Rabiei","sequence":"first","affiliation":[{"name":"International University of Sarajevo, Engineering and Natural Sciences , Sarajevo , Bosnia and Herzegovina"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Elias G.","family":"Saleeby","sequence":"additional","affiliation":[{"name":"Mount Lebanon , Lebanon"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2021,4,30]]},"reference":[{"key":"2021053122092001103_j_mcma-2021-2087_ref_001_w2aab3b7e1650b1b6b1ab2b1b1Aa","doi-asserted-by":"crossref","unstructured":"S.  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D.  Hanebek,\nA direct method for checking overlap of two hyperellipsoids,\n2014 Sensor Data Fusion, Trends, Solutions and Applications,\nIEEE Press, Piscataway (2014), 1\u20136.","DOI":"10.1109\/SDF.2014.6954724"},{"key":"2021053122092001103_j_mcma-2021-2087_ref_008_w2aab3b7e1650b1b6b1ab2b1b8Aa","doi-asserted-by":"crossref","unstructured":"U.  Jaekel,\nA Monte Calro method for high-dimensional volume estimation and application to polytopes,\nProcedia Comp. Sci. 4 (2011), 1403\u20131411.","DOI":"10.1016\/j.procs.2011.04.151"},{"key":"2021053122092001103_j_mcma-2021-2087_ref_009_w2aab3b7e1650b1b6b1ab2b1b9Aa","unstructured":"M. G.  Kendall and P. A. P.  Moran,\nGeometrical Probability,\nHafner, New York, 1963."},{"key":"2021053122092001103_j_mcma-2021-2087_ref_010_w2aab3b7e1650b1b6b1ab2b1c10Aa","doi-asserted-by":"crossref","unstructured":"T. H.  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