{"id":275,"date":"2023-06-13T13:10:57","date_gmt":"2023-06-13T20:10:57","guid":{"rendered":"https:\/\/live-usc-dornsife.pantheonsite.io\/larry-goldstein\/?page_id=275"},"modified":"2023-06-20T12:59:17","modified_gmt":"2023-06-20T19:59:17","slug":"math-541b-introduction-to-mathematical-statistics","status":"publish","type":"page","link":"https:\/\/dornsife.usc.edu\/larry-goldstein\/math-541b-introduction-to-mathematical-statistics\/","title":{"rendered":"Math 541b &#8211; Introduction to Mathematical Statistics"},"content":{"rendered":"\n\n  \n    \n\n\n\n\n\n\n<div\n  class=\"cc--component-container cc--rich-text \"\n\n  \n  \n  \n  \n  \n  \n  >\n  <div class=\"c--component c--rich-text\"\n    \n      >\n\n    \n      \n<div class=\"f--field f--wysiwyg\">\n\n    \n  <h5>Course Content:<\/h5>\n<ul>\n<li>Hypotheses testing<\/li>\n<\/ul>\n<div>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Neyman-Pearson lemma, Uniformly most powerful tests, consistency, power<br \/>\nConfidence intervals and interval estimation<br \/>\nThe Generalized Likelihood Ratio Procedure and its large sample behavior, goodness of fit tests.<\/div>\n<ul>\n<li>Computationally intensive methods in statistics<\/li>\n<\/ul>\n<div>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Resampling schemes, jackknife and bootstrap<br \/>\nEM algorithm<br \/>\nMonte Carlo Markov Chain methods.<\/div>\n<ul>\n<li>Additional topics as time permits<\/li>\n<\/ul>\n<p><strong>Instructor<\/strong>:\u00a0<a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/\">Larry Goldstein<\/a>, KAP 406D, larry at math dot usc dot edu, (213) 740 -2405<br \/>\n<strong>Office Hours:<\/strong>\u00a0Monday 10-11, Friday 1-2:30<\/p>\n<p><strong>Grader:<\/strong>\u00a0Panagiotis Tsilifis. KAP 446. tsilifis at usc dot edu, (213) 234-8642<br \/>\n<strong>Office Hours:<\/strong>\u00a0MW 9-10 and W 1-2 in the\u00a0<big><a href=\"https:\/\/dornsife.usc.edu\/mathcenter\/\">Math Center<\/a><\/big><\/p>\n<p>Lecture 39750R, MWF 11-11:50, KAP-148<\/p>\n<p><big>See the\u00a0<a href=\"https:\/\/classes.usc.edu\/term-20143\/calendar\/\">registration calendar<\/a>\u00a0for important (drop) dates.\u00a0 \u00a0<\/big><\/p>\n\n\n\n<\/div>\n\n\n  <\/div><\/div>\n\n\n\n\n  \n    \n\n\n\n\n\n\n<div\n  class=\"cc--component-container cc--rich-text \"\n\n  \n  \n  \n  \n  \n  \n  >\n  <div class=\"c--component c--rich-text\"\n    \n      >\n\n    \n      \n<div class=\"f--field f--wysiwyg\">\n\n    \n  <p><center><\/p>\n<h5 style=\"text-align: left;\">Texts and References<\/h5>\n<p><\/center><strong>Required Text:<\/strong><br \/>\nStatistical Inference, by Casella and Berger.<\/p>\n<p><strong>Recommended Text:\u00a0<\/strong><br \/>\nA Course in Large Sample Theory. Tom Ferguson.<\/p>\n<p><strong>Classic Text on Hypothesis testing:\u00a0<\/strong>Testing Statistical Hypotheses, Erich Lehmann<\/p>\n<p><strong>References: Computationally Intensive Methods<\/strong><\/p>\n<p><strong>Resampling\u00a0<\/strong><\/p>\n<ul>\n<li>The Jackknife, the Bootstrap and Other Resampling Plans. Bradley Efron<\/li>\n<li>The Jackknife and Bootstrap. Jun Shao.<\/li>\n<li>When does bootstrap work? : Asymptotic results and simulations. E. Mammen<\/li>\n<\/ul>\n<p><strong>\u00a0EM Algorithm<\/strong><\/p>\n<ul>\n<li>The EM Algorithm and Extensions. McLachlan and Krishnan<\/li>\n<li>On the convergence properties of the EM algorithm. C.F.J. Wu. The Annals of Statistics, 1983 vol. 11, pp 95-103\u00a0<a href=\"http:\/\/www.ams.org\/mathscinet\/pdf\/684867.pdf?arg3=&amp;co4=AND&amp;co5=AND&amp;co6=AND&amp;co7=AND&amp;dr=all&amp;mx-pid=684867&amp;pg4=TI&amp;pg5=AUCN&amp;pg6=PC&amp;pg7=ALLF&amp;pg8=ET&amp;r=9&amp;review_format=html&amp;s4=EM&amp;s5=Wu&amp;s6=&amp;s7=&amp;s8=All&amp;vfpref=html&amp;yearRangeFirst=&amp;yearRangeSecond=&amp;yrop=eq\">MR0684867 (85e:62049)<\/a><\/li>\n<\/ul>\n<p><strong>Monte Carlo Markov Chains<\/strong><\/p>\n<ul>\n<li>Finite Markov Chains and Algorithmic Applications. Olle H\u00e4ggstr\u00f6m<\/li>\n<li>Monte Carlo Statistical Methods, Christian Robert, George Casella<\/li>\n<\/ul>\n<p>The birth of MCMC:<br \/>\n<a href=\"http:\/\/jcp.aip.org\/resource\/1\/jcpsa6\/v21\/i6\/p1087_s1\">Equation of State Calculation by Fast Computing Machines<\/a>, Metropolis, Rosenbluth, Rosenbluth, Teller, and Teller.<\/p>\n\n\n\n<\/div>\n\n\n  <\/div><\/div>\n\n\n\n\n  \n    \n\n\n\n\n\n\n<div\n  class=\"cc--component-container cc--rich-text \"\n\n  \n  \n  \n  \n  \n  \n  >\n  <div class=\"c--component c--rich-text\"\n    \n      >\n\n    \n      \n<div class=\"f--field f--wysiwyg\">\n\n    \n  <h5>Exams and Grading Policy<\/h5>\n<ul>\n<li>Homework:\u00a0 20%<\/li>\n<li>Midterm I,\u00a0 25%: Friday, October 10th. Will cover all material on testing hypotheses, and interval estimation. The exam will be closed book, closed notes.<\/li>\n<\/ul>\n<p>25<sup>th<\/sup>\u00a0percentile 105, median 180, 75<sup>th<\/sup>\u00a0percentile 277, high score 300<\/p>\n<ul>\n<li>Midterm II, 25%: Friday, November 7th. Will cover resampling schemes. Closed book, closed notes.<\/li>\n<\/ul>\n<p>25<sup>th<\/sup>\u00a0percentile 123, median 165, 75<sup>th<\/sup>\u00a0percentile 189, three high scores of 200<\/p>\n<ul>\n<li>Final Exam, 30%, Wednesday, December 10th, 11-1; will be comprehensive, with possible emphasis on material not covered in the first two midterms.<\/li>\n<\/ul>\n\n\n\n<\/div>\n\n\n  <\/div><\/div>\n\n\n\n\n  \n    \n\n\n\n\n\n\n<div\n  class=\"cc--component-container cc--rich-text \"\n\n  \n  \n  \n  \n  \n  \n  >\n  <div class=\"c--component c--rich-text\"\n    \n      >\n\n    \n      \n<div class=\"f--field f--wysiwyg\">\n\n    \n  <p><center><\/p>\n<h5 style=\"text-align: left;\"><strong>Homework<\/strong><\/h5>\n<p><\/center>Due dates are not finalized until they appear in\u00a0bold. All homework is due in Grader&#8217;s mailbox in math graduate student lounge, 4th floor KAP.<\/p>\n<p>Cramer-Rao: 3,4,5 Due Tuesday\u00a09\/9<br \/>\nChapter 8: 1,2,12,13,14,15.\u00a0 Due Tuesday\u00a09\/16<br \/>\nChapter 8: 5, 6, 8,17, 28,33, 34, 46, and Problem Set #1, due Friday\u00a010\/10<br \/>\nChapter 9: 2,3a,4,5,9, due Tuesday\u00a010\/14<br \/>\nProblem Set #2, due Thursday\u00a010\/30<br \/>\nProblem Set #3, due Thursday\u00a011\/20<\/p>\n\n\n\n<\/div>\n\n\n  <\/div><\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":370,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"footnotes":""},"class_list":["post-275","page","type-page","status-publish","hentry"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.1.1 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Math 541b - Introduction to Mathematical Statistics - Larry Goldstein<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/math-541b-introduction-to-mathematical-statistics\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Math 541b - Introduction to Mathematical Statistics - Larry Goldstein\" \/>\n<meta property=\"og:url\" content=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/math-541b-introduction-to-mathematical-statistics\/\" \/>\n<meta property=\"og:site_name\" content=\"Larry Goldstein\" \/>\n<meta property=\"article:modified_time\" content=\"2023-06-20T19:59:17+00:00\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/dornsife.usc.edu\/larry-goldstein\/math-541b-introduction-to-mathematical-statistics\/\",\"url\":\"https:\/\/dornsife.usc.edu\/larry-goldstein\/math-541b-introduction-to-mathematical-statistics\/\",\"name\":\"Math 541b - Introduction to Mathematical Statistics - Larry Goldstein\",\"isPartOf\":{\"@id\":\"https:\/\/dornsife.usc.edu\/larry-goldstein\/#website\"},\"datePublished\":\"2023-06-13T20:10:57+00:00\",\"dateModified\":\"2023-06-20T19:59:17+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/dornsife.usc.edu\/larry-goldstein\/math-541b-introduction-to-mathematical-statistics\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/dornsife.usc.edu\/larry-goldstein\/math-541b-introduction-to-mathematical-statistics\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/dornsife.usc.edu\/larry-goldstein\/math-541b-introduction-to-mathematical-statistics\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/dornsife.usc.edu\/larry-goldstein\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Math 541b &#8211; 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