{"id":399,"date":"2019-01-01T05:04:41","date_gmt":"2019-01-01T05:04:41","guid":{"rendered":"http:\/\/statp12.epgpbooks.inflibnet.ac.in\/?post_type=chapter&#038;p=399"},"modified":"2019-01-01T05:04:43","modified_gmt":"2019-01-01T05:04:43","slug":"some-properties-of-em-algorithm","status":"publish","type":"chapter","link":"https:\/\/ebooks.inflibnet.ac.in\/statp12\/chapter\/some-properties-of-em-algorithm\/","title":{"rendered":"Some properties of EM algorithm"},"content":{"raw":"<div class=\"textLayer\">\r\n<div><img class=\"aligncenter size-full wp-image-400\" src=\"http:\/\/statp12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/140\/2019\/01\/9500_et_missing_data_6_em_properties-03.jpg\" alt=\"\" width=\"784\" height=\"178\" \/> <img class=\"aligncenter size-full wp-image-401\" src=\"http:\/\/statp12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/140\/2019\/01\/9500_et_missing_data_6_em_properties-04.jpg\" alt=\"\" width=\"704\" height=\"386\" \/> <img class=\"aligncenter size-full wp-image-402\" src=\"http:\/\/statp12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/140\/2019\/01\/9500_et_missing_data_6_em_properties-05.jpg\" alt=\"\" width=\"810\" height=\"363\" \/> <img class=\"aligncenter size-full wp-image-403\" src=\"http:\/\/statp12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/140\/2019\/01\/9500_et_missing_data_6_em_properties-06.jpg\" alt=\"\" width=\"859\" height=\"517\" \/> <img class=\"aligncenter size-full wp-image-404\" src=\"http:\/\/statp12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/140\/2019\/01\/9500_et_missing_data_6_em_properties-07.jpg\" alt=\"\" width=\"871\" height=\"556\" \/> <img class=\"aligncenter size-full wp-image-405\" src=\"http:\/\/statp12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/140\/2019\/01\/9500_et_missing_data_6_em_properties-08.jpg\" alt=\"\" width=\"879\" height=\"426\" \/> <img class=\"aligncenter size-full wp-image-406\" src=\"http:\/\/statp12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/140\/2019\/01\/9500_et_missing_data_6_em_properties-09.jpg\" alt=\"\" width=\"895\" height=\"604\" \/> <img class=\"aligncenter size-full wp-image-407\" src=\"http:\/\/statp12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/140\/2019\/01\/9500_et_missing_data_6_em_properties-10.jpg\" alt=\"\" width=\"858\" height=\"419\" \/><\/div>\r\n<div><\/div>\r\n<div>References<\/div>\r\n<ul>\r\n \t<li style=\"text-align: justify\">Little, R.J.A. and Rubin, D.B. (1987). Statistical Analysis with Missing Data. New York: Wiley; Chapter 7<\/li>\r\n \t<li style=\"text-align: justify\">McLachlan, G.J and Krishnan T (1997). The EM Algorithm and Extensions.John Wiley Sons, Inc.<\/li>\r\n \t<li style=\"text-align: justify\">Dempster, A.P., Laird, N.M., and Rubin, D.B. (1977). Maximum likelihood estimation from incomplete data via the EM algorithm. Journal of The Royal Statistical Society, Series B, 39, 1-38<\/li>\r\n<\/ul>\r\n<\/div>","rendered":"<div class=\"textLayer\">\n<div><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-400\" src=\"http:\/\/statp12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/140\/2019\/01\/9500_et_missing_data_6_em_properties-03.jpg\" alt=\"\" width=\"784\" height=\"178\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9500_et_missing_data_6_em_properties-03.jpg 784w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9500_et_missing_data_6_em_properties-03-300x68.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9500_et_missing_data_6_em_properties-03-768x174.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9500_et_missing_data_6_em_properties-03-65x15.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9500_et_missing_data_6_em_properties-03-225x51.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9500_et_missing_data_6_em_properties-03-350x79.jpg 350w\" sizes=\"auto, (max-width: 784px) 100vw, 784px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-401\" src=\"http:\/\/statp12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/140\/2019\/01\/9500_et_missing_data_6_em_properties-04.jpg\" alt=\"\" width=\"704\" height=\"386\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9500_et_missing_data_6_em_properties-04.jpg 704w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9500_et_missing_data_6_em_properties-04-300x164.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9500_et_missing_data_6_em_properties-04-65x36.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9500_et_missing_data_6_em_properties-04-225x123.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9500_et_missing_data_6_em_properties-04-350x192.jpg 350w\" sizes=\"auto, (max-width: 704px) 100vw, 704px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-402\" src=\"http:\/\/statp12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/140\/2019\/01\/9500_et_missing_data_6_em_properties-05.jpg\" alt=\"\" width=\"810\" height=\"363\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9500_et_missing_data_6_em_properties-05.jpg 810w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9500_et_missing_data_6_em_properties-05-300x134.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9500_et_missing_data_6_em_properties-05-768x344.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9500_et_missing_data_6_em_properties-05-65x29.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9500_et_missing_data_6_em_properties-05-225x101.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9500_et_missing_data_6_em_properties-05-350x157.jpg 350w\" sizes=\"auto, (max-width: 810px) 100vw, 810px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-403\" src=\"http:\/\/statp12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/140\/2019\/01\/9500_et_missing_data_6_em_properties-06.jpg\" alt=\"\" width=\"859\" height=\"517\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9500_et_missing_data_6_em_properties-06.jpg 859w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9500_et_missing_data_6_em_properties-06-300x181.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9500_et_missing_data_6_em_properties-06-768x462.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9500_et_missing_data_6_em_properties-06-65x39.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9500_et_missing_data_6_em_properties-06-225x135.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9500_et_missing_data_6_em_properties-06-350x211.jpg 350w\" sizes=\"auto, (max-width: 859px) 100vw, 859px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-404\" src=\"http:\/\/statp12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/140\/2019\/01\/9500_et_missing_data_6_em_properties-07.jpg\" alt=\"\" width=\"871\" height=\"556\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9500_et_missing_data_6_em_properties-07.jpg 871w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9500_et_missing_data_6_em_properties-07-300x192.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9500_et_missing_data_6_em_properties-07-768x490.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9500_et_missing_data_6_em_properties-07-65x41.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9500_et_missing_data_6_em_properties-07-225x144.jpg 225w, 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alt=\"\" width=\"858\" height=\"419\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9500_et_missing_data_6_em_properties-10.jpg 858w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9500_et_missing_data_6_em_properties-10-300x147.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9500_et_missing_data_6_em_properties-10-768x375.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9500_et_missing_data_6_em_properties-10-65x32.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9500_et_missing_data_6_em_properties-10-225x110.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-content\/uploads\/sites\/140\/2019\/01\/9500_et_missing_data_6_em_properties-10-350x171.jpg 350w\" sizes=\"auto, (max-width: 858px) 100vw, 858px\" \/><\/div>\n<div><\/div>\n<div>References<\/div>\n<ul>\n<li style=\"text-align: justify\">Little, R.J.A. and Rubin, D.B. (1987). Statistical Analysis with Missing Data. New York: Wiley; Chapter 7<\/li>\n<li style=\"text-align: justify\">McLachlan, G.J and Krishnan T (1997). The EM Algorithm and Extensions.John Wiley Sons, Inc.<\/li>\n<li style=\"text-align: justify\">Dempster, A.P., Laird, N.M., and Rubin, D.B. (1977). Maximum likelihood estimation from incomplete data via the EM algorithm. Journal of The Royal Statistical Society, Series B, 39, 1-38<\/li>\n<\/ul>\n<\/div>\n","protected":false},"author":3,"menu_order":20,"template":"","meta":{"_acf_changed":false,"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":["souvik-kumar-bandyopadhyay"],"pb_section_license":""},"chapter-type":[],"contributor":[58],"license":[],"class_list":["post-399","chapter","type-chapter","status-publish","hentry","contributor-souvik-kumar-bandyopadhyay"],"part":3,"_links":{"self":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-json\/pressbooks\/v2\/chapters\/399","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-json\/wp\/v2\/users\/3"}],"version-history":[{"count":1,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-json\/pressbooks\/v2\/chapters\/399\/revisions"}],"predecessor-version":[{"id":408,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-json\/pressbooks\/v2\/chapters\/399\/revisions\/408"}],"part":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-json\/pressbooks\/v2\/chapters\/399\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-json\/wp\/v2\/media?parent=399"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-json\/pressbooks\/v2\/chapter-type?post=399"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-json\/wp\/v2\/contributor?post=399"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp12\/wp-json\/wp\/v2\/license?post=399"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}