{"id":829,"date":"2019-01-03T11:34:30","date_gmt":"2019-01-03T11:34:30","guid":{"rendered":"http:\/\/statp06.epgpbooks.inflibnet.ac.in\/?post_type=chapter&#038;p=829"},"modified":"2019-01-03T11:34:30","modified_gmt":"2019-01-03T11:34:30","slug":"some-important-theorems-on-mle","status":"publish","type":"chapter","link":"https:\/\/ebooks.inflibnet.ac.in\/statp06\/chapter\/some-important-theorems-on-mle\/","title":{"rendered":"Some Important Theorems on MLE"},"content":{"raw":"<div><span style=\"float: right\"><a href=\"https:\/\/youtu.be\/fiDeeZECWmA\" target=\"_blank\" rel=\"noopener\"><img src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"epgp books\" width=\"75px\" height=\"75px;\" \/><\/a>\r\n<\/span><\/div>\r\n<img class=\"aligncenter size-full wp-image-830\" src=\"http:\/\/statp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_02.jpg\" alt=\"\" width=\"1507\" height=\"855\" \/> <img class=\"aligncenter size-full wp-image-831\" src=\"http:\/\/statp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_03.jpg\" alt=\"\" width=\"1511\" height=\"873\" \/> <img class=\"aligncenter size-full wp-image-832\" src=\"http:\/\/statp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_04.jpg\" alt=\"\" width=\"1511\" height=\"437\" \/> <img class=\"aligncenter size-full wp-image-833\" src=\"http:\/\/statp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_05.jpg\" alt=\"\" width=\"1511\" height=\"659\" \/> <img class=\"aligncenter size-full wp-image-834\" src=\"http:\/\/statp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_06.jpg\" alt=\"\" width=\"1511\" height=\"661\" \/> <img class=\"aligncenter size-full wp-image-835\" src=\"http:\/\/statp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_07.jpg\" alt=\"\" width=\"1511\" height=\"161\" \/> <img class=\"aligncenter size-full wp-image-836\" src=\"http:\/\/statp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_08.jpg\" alt=\"\" width=\"1511\" height=\"377\" \/> <img class=\"aligncenter size-full wp-image-837\" src=\"http:\/\/statp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_09.jpg\" alt=\"\" width=\"1511\" height=\"365\" \/> <img class=\"aligncenter size-full wp-image-838\" src=\"http:\/\/statp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_10.jpg\" alt=\"\" width=\"1511\" height=\"795\" \/> <img class=\"aligncenter size-full wp-image-839\" src=\"http:\/\/statp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_11.jpg\" alt=\"\" width=\"1509\" height=\"607\" \/> <img class=\"aligncenter size-full wp-image-840\" src=\"http:\/\/statp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_12.jpg\" alt=\"\" width=\"1509\" height=\"903\" \/> <img class=\"aligncenter size-full wp-image-841\" src=\"http:\/\/statp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_13.jpg\" alt=\"\" width=\"1511\" height=\"755\" \/> <img class=\"aligncenter size-full wp-image-842\" src=\"http:\/\/statp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_14.jpg\" alt=\"\" width=\"1511\" height=\"795\" \/> <img class=\"aligncenter size-full wp-image-843\" src=\"http:\/\/statp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_15.jpg\" alt=\"\" width=\"1509\" height=\"391\" \/> <img class=\"aligncenter size-full wp-image-844\" src=\"http:\/\/statp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_16.jpg\" alt=\"\" width=\"1509\" height=\"423\" \/> <img class=\"aligncenter size-full wp-image-845\" src=\"http:\/\/statp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_17.jpg\" alt=\"\" width=\"1511\" height=\"535\" \/> <img class=\"aligncenter size-full wp-image-846\" src=\"http:\/\/statp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_18.jpg\" alt=\"\" width=\"1511\" height=\"445\" \/> <img class=\"aligncenter size-full wp-image-847\" src=\"http:\/\/statp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_19.jpg\" alt=\"\" width=\"1511\" height=\"935\" \/> <img class=\"aligncenter size-full wp-image-848\" src=\"http:\/\/statp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_20.jpg\" alt=\"\" width=\"1511\" height=\"801\" \/> <img class=\"aligncenter size-full wp-image-849\" src=\"http:\/\/statp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_21.jpg\" alt=\"\" width=\"1511\" height=\"575\" \/> <img class=\"aligncenter size-full wp-image-850\" src=\"http:\/\/statp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_22.jpg\" alt=\"\" width=\"1511\" height=\"893\" \/> <img class=\"aligncenter size-full wp-image-851\" src=\"http:\/\/statp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_23.jpg\" alt=\"\" width=\"1509\" height=\"589\" \/> <img class=\"aligncenter size-full wp-image-852\" src=\"http:\/\/statp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_24.jpg\" alt=\"\" width=\"1509\" height=\"339\" \/> <img class=\"aligncenter size-full wp-image-853\" src=\"http:\/\/statp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_25.jpg\" alt=\"\" width=\"1511\" height=\"545\" \/>\r\n<table width=\"700\">\r\n<tbody>\r\n<tr>\r\n<td><strong>You can view video on Some Important Theorems on MLE<\/strong><\/td>\r\n<td><a href=\"https:\/\/youtu.be\/fiDeeZECWmA\"><img class=\"alignnone wp-image-120\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"\" width=\"36\" height=\"36\" \/><\/a><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n&nbsp;\r\n\r\n<strong>References:<\/strong>\r\n<ol>\r\n \t<li style=\"text-align: justify\">Theory of Point Estimation, Second Edition: Lehmann, E. L. and Casella, G.<\/li>\r\n \t<li style=\"text-align: justify\">An Outline of Statistics,Volume 2: Goon, A. M., Gupta, M. and Dasgupta, B.<\/li>\r\n \t<li style=\"text-align: justify\">Statistical Inference,Second Edition: Casella, G. and Berger, R. L.<\/li>\r\n \t<li style=\"text-align: justify\">A First Course on Parametric Inference,Second Edition: Kale, B. K.<\/li>\r\n \t<li style=\"text-align: justify\">Mathematical Methods of Statistics : Cramer, H.<\/li>\r\n \t<li style=\"text-align: justify\">Kulldorf, G. (1957) :On the condition for consistency and asymptoticeciency of maximum likelihood estimates,Skand. Aktusrietidskr.40, 129 { 144.<\/li>\r\n<\/ol>","rendered":"<div><span style=\"float: right\"><a href=\"https:\/\/youtu.be\/fiDeeZECWmA\" target=\"_blank\" rel=\"noopener\"><img decoding=\"async\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"epgp books\" width=\"75px\" height=\"75px;\" \/><\/a><br \/>\n<\/span><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-830\" src=\"http:\/\/statp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_02.jpg\" alt=\"\" width=\"1507\" height=\"855\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_02.jpg 1507w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_02-300x170.jpg 300w, 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height=\"873\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_03.jpg 1511w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_03-300x173.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_03-768x444.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_03-1024x592.jpg 1024w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_03-65x38.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_03-225x130.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_03-350x202.jpg 350w\" sizes=\"auto, (max-width: 1511px) 100vw, 1511px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-832\" src=\"http:\/\/statp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_04.jpg\" alt=\"\" width=\"1511\" height=\"437\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_04.jpg 1511w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_04-300x87.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_04-768x222.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_04-1024x296.jpg 1024w, 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sizes=\"auto, (max-width: 1511px) 100vw, 1511px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-835\" src=\"http:\/\/statp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_07.jpg\" alt=\"\" width=\"1511\" height=\"161\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_07.jpg 1511w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_07-300x32.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_07-768x82.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_07-1024x109.jpg 1024w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_07-65x7.jpg 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sizes=\"auto, (max-width: 1509px) 100vw, 1509px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-841\" src=\"http:\/\/statp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_13.jpg\" alt=\"\" width=\"1511\" height=\"755\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_13.jpg 1511w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_13-300x150.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_13-768x384.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_13-1024x512.jpg 1024w, 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src=\"http:\/\/statp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_18.jpg\" alt=\"\" width=\"1511\" height=\"445\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_18.jpg 1511w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_18-300x88.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_18-768x226.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_18-1024x302.jpg 1024w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_18-65x19.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_18-225x66.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_18-350x103.jpg 350w\" sizes=\"auto, (max-width: 1511px) 100vw, 1511px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-847\" src=\"http:\/\/statp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_19.jpg\" alt=\"\" width=\"1511\" height=\"935\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_19.jpg 1511w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_19-300x186.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_19-768x475.jpg 768w, 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srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_20.jpg 1511w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_20-300x159.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_20-768x407.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_20-1024x543.jpg 1024w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_20-65x34.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_20-225x119.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_20-350x186.jpg 350w\" sizes=\"auto, (max-width: 1511px) 100vw, 1511px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-849\" src=\"http:\/\/statp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_21.jpg\" alt=\"\" width=\"1511\" height=\"575\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_21.jpg 1511w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_21-300x114.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_21-768x292.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_21-1024x390.jpg 1024w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_21-65x25.jpg 65w, 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https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_22-768x454.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_22-1024x605.jpg 1024w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_22-65x38.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_22-225x133.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_22-350x207.jpg 350w\" sizes=\"auto, (max-width: 1511px) 100vw, 1511px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-851\" src=\"http:\/\/statp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_23.jpg\" alt=\"\" width=\"1509\" height=\"589\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_23.jpg 1509w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_23-300x117.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_23-768x300.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_23-1024x400.jpg 1024w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_23-65x25.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_23-225x88.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_23-350x137.jpg 350w\" sizes=\"auto, (max-width: 1509px) 100vw, 1509px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-852\" src=\"http:\/\/statp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_24.jpg\" alt=\"\" width=\"1509\" height=\"339\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_24.jpg 1509w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_24-300x67.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_24-768x173.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_24-1024x230.jpg 1024w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_24-65x15.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_24-225x51.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_24-350x79.jpg 350w\" sizes=\"auto, (max-width: 1509px) 100vw, 1509px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-853\" src=\"http:\/\/statp06.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_25.jpg\" alt=\"\" width=\"1511\" height=\"545\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_25.jpg 1511w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_25-300x108.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_25-768x277.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_25-1024x369.jpg 1024w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_25-65x23.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_25-225x81.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-content\/uploads\/sites\/133\/2019\/01\/1465558901Module7Quadrant1_Page_25-350x126.jpg 350w\" sizes=\"auto, (max-width: 1511px) 100vw, 1511px\" \/><\/p>\n<table style=\"width: 700px;\">\n<tbody>\n<tr>\n<td><strong>You can view video on Some Important Theorems on MLE<\/strong><\/td>\n<td><a href=\"https:\/\/youtu.be\/fiDeeZECWmA\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-120\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"\" width=\"36\" height=\"36\" \/><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p><strong>References:<\/strong><\/p>\n<ol>\n<li style=\"text-align: justify\">Theory of Point Estimation, Second Edition: Lehmann, E. L. and Casella, G.<\/li>\n<li style=\"text-align: justify\">An Outline of Statistics,Volume 2: Goon, A. M., Gupta, M. and Dasgupta, B.<\/li>\n<li style=\"text-align: justify\">Statistical Inference,Second Edition: Casella, G. and Berger, R. L.<\/li>\n<li style=\"text-align: justify\">A First Course on Parametric Inference,Second Edition: Kale, B. K.<\/li>\n<li style=\"text-align: justify\">Mathematical Methods of Statistics : Cramer, H.<\/li>\n<li style=\"text-align: justify\">Kulldorf, G. (1957) :On the condition for consistency and asymptoticeciency of maximum likelihood estimates,Skand. Aktusrietidskr.40, 129 { 144.<\/li>\n<\/ol>\n","protected":false},"author":4,"menu_order":27,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":["saurav-de"],"pb_section_license":""},"chapter-type":[],"contributor":[59],"license":[],"class_list":["post-829","chapter","type-chapter","status-publish","hentry","contributor-saurav-de"],"part":3,"_links":{"self":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-json\/pressbooks\/v2\/chapters\/829","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-json\/wp\/v2\/users\/4"}],"version-history":[{"count":1,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-json\/pressbooks\/v2\/chapters\/829\/revisions"}],"predecessor-version":[{"id":854,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-json\/pressbooks\/v2\/chapters\/829\/revisions\/854"}],"part":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-json\/pressbooks\/v2\/chapters\/829\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-json\/wp\/v2\/media?parent=829"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-json\/pressbooks\/v2\/chapter-type?post=829"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-json\/wp\/v2\/contributor?post=829"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp06\/wp-json\/wp\/v2\/license?post=829"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}