{"id":307,"date":"2023-06-13T13:32:56","date_gmt":"2023-06-13T20:32:56","guid":{"rendered":"https:\/\/live-usc-dornsife.pantheonsite.io\/larry-goldstein\/?page_id=307"},"modified":"2023-06-20T13:01:49","modified_gmt":"2023-06-20T20:01:49","slug":"mathematical-statistics-3","status":"publish","type":"page","link":"https:\/\/dornsife.usc.edu\/larry-goldstein\/mathematical-statistics-3\/","title":{"rendered":"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  <p>With the advent of powerful computing and the availability of massive sets of data, statistics has become a valuable tool in numerous applications. This course covers the basics of advanced mathematical statistics, both classical and modern.<\/p>\n<ul>\n<li>Review of basic probability<\/li>\n<li>Parametric models, linear models, variable selection<\/li>\n<li>Estimation: criteria and construction of estimators, maximum likelihood, asymptotics<\/li>\n<li>Hypothesis testing, multiple hypotheses testing<\/li>\n<li>Non parametric models, empirical distribution function, jackknife and bootstrap, non-parametric testing, density and regression estimation<\/li>\n<li>Classification: discriminant analysis, support vector machines, multivariate analysis, EM algorithm and simulation including Monte Carlo Markov Chain<\/li>\n<\/ul>\n<p>The level and detailed content of the course will be determined along with the students according to their background and interests.<\/p>\n<p><big><strong>Prerequisite:<\/strong>\u00a0At least one good course in probability, and some basic statistics.<br \/>\n<strong>Instructors:\u00a0<\/strong><\/big><big><a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/\">Larry Goldstein<\/a>\u00a0and\u00a0<a href=\"https:\/\/www.fam.tuwien.ac.at\/~schmock\/\">Uwe Schmock<\/a><\/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  <h2>Structure and Evaluation<\/h2>\n<p><strong>First week quiz<\/strong>: percentiles, out 90 points total: 25th: 12, median: 35, 75th: 54<br \/>\n<strong>Midterm:<\/strong>\u00a030% scores: 26, 30, 41, 43, 55, 55, 58, 59, 62, 65, 67 Solutions<br \/>\n<strong>Final Exam<\/strong>: 45%<br \/>\n<strong>Course participation:<\/strong>\u00a025%<\/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>&nbsp;<\/p>\n<h2 style=\"text-align: left;\"><strong>Course Text<\/strong><\/h2>\n<p style=\"text-align: left;\">All of Statistics: A concise course in Statistical Inference, by\u00a0Larry Wasserman.<\/p>\n<p><strong><big><big>Additional References<\/big><\/big><\/strong><\/p>\n<ul>\n<li>Mathematical Statistics: Basic Ideas and Selected Topics, by Peter Bickel and Kjell Doksum<\/li>\n<li><big>A Course in Large Sample Theory, by Thomas Ferguson<\/big><\/li>\n<\/ul>\n<p><strong><big><big>Links of Interest<\/big><\/big><\/strong><\/p>\n<p><a href=\"https:\/\/en.wikipedia.org\/wiki\/Benford%27s_law\">Benford&#8217;s law<\/a>,\u00a0<a href=\"https:\/\/www.stat.auckland.ac.nz\/~fewster\/RFewster_Benford.pdf\">Simple Explanation<\/a>,\u00a0<a href=\"https:\/\/projecteuclid.org\/euclid.ps\/1311860830\">Basic Theory of Benford&#8217;s law<\/a>\u00a0(for scale invariance, see Example 4.19 on page 42)<br \/>\n<a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2023\/06\/DEU-10m-anv.jpg\">Formula for one dimensional normal density<\/a><br \/>\n<a href=\"https:\/\/en.wikipedia.org\/wiki\/Box%E2%80%93Muller_transform\">Box Muller Transformation<\/a><br \/>\n<a href=\"https:\/\/www.skylinewebcams.com\/it\/webcam\/italia\/umbria\/perugia\/piazza-iv-novembre.html\">Perugia Web Cam, Piazza IV novembre<\/a><\/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  <h2>Exercises<\/h2>\n<p><a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2023\/06\/set1.pdf\"><big>Exercise Set 1<\/big><big><big><br \/>\n<\/big><\/big><\/a><a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2023\/06\/set2.pdf\"><big>Exercise Set 2<\/big><big><\/big><\/a><br \/>\n<a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2023\/06\/set3.pdf\"><big>Exercise Set 3<\/big><\/a><big><br \/>\n<a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2023\/06\/set4.pdf\">Exercise Set 4<\/a><br \/>\n<\/big><a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2023\/06\/set5.pdf\"><big>Exercise Set 5<br \/>\n<\/big><\/a><a href=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/wp-content\/uploads\/sites\/221\/2023\/06\/set6.pdf\"><big>Exercise Set 6<\/big><\/a><\/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-307","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>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\/mathematical-statistics-3\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Mathematical Statistics - Larry Goldstein\" \/>\n<meta property=\"og:url\" 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