{"id":247,"date":"2023-06-13T12:58:31","date_gmt":"2023-06-13T19:58:31","guid":{"rendered":"https:\/\/live-usc-dornsife.pantheonsite.io\/larry-goldstein\/?page_id=247"},"modified":"2023-06-20T12:56:45","modified_gmt":"2023-06-20T19:56:45","slug":"math-541a-introduction-to-mathematical-statistics-spring-2013","status":"publish","type":"page","link":"https:\/\/dornsife.usc.edu\/larry-goldstein\/math-541a-introduction-to-mathematical-statistics-spring-2013\/","title":{"rendered":"Math 541a &#8211; Introduction to Mathematical Statistics &#8211; Spring 2013"},"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><strong>Course Content:<\/strong><\/p>\n<ul>\n<li>Statistical models, Parametric families of distributions, multivariate distributions including the normal, order statistics.<\/li>\n<li>Data reduction, sufficiency, completeness, exponential families.<\/li>\n<li>Mixtures, inequalities, convergence concepts, sampling and derived distributions from a normal population.<\/li>\n<li>Estimation: unbiased estimation, substitution principles, method of moments, least squares, maximum likelihood, asymptotics.<\/li>\n<li>Comparison of estimators, optimality, information inequality, large sample behavior, consistency, convergence in distribution, asymptotic efficiency.<\/li>\n<li>Additional topics as time permits.<\/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><strong>Prerequisites:<\/strong>\u00a0Probability at the Math 505a level, or equivalent, multivariate calculus and linear algebra.<\/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><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<\/p>\n<p><strong>Office Hours:<\/strong>\u00a0Monday 12:50-1:50, Friday 2-3<\/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><strong>Grader:<\/strong>\u00a0Jerome Grand&#8217;Maison<\/p>\n<p><strong>Office Hours:<\/strong>\u00a08-11, Friday at the\u00a0<a href=\"https:\/\/dornsife.usc.edu\/mathcenter\/\">Math Center<\/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  <p><strong>Lecture:<\/strong>\u00a039760R,\u00a0 MWF 11:00 &#8211; 11:50,\u00a0 THH 116<\/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>Materials<\/h5>\n<p><strong>Primary Text: &#8211;\u00a0<\/strong>Statistical Inference, by Casella and Berger, 2nd Edition.<\/p>\n<p><strong>Supplemental References: &#8211;<\/strong><\/p>\n<ul>\n<li>Statistical Inference by Garthwaite, Jolliffe and Jones, Oxford Scientific.<\/li>\n<li>A Course in Large Sample Theory, by Ferguson.<\/li>\n<li>Mathematical Statistics, by Bickel and Doksum<\/li>\n<li>Asymptotic Statistics, by van der Vaart<\/li>\n<li>Theory of Point Estimation, by E.L.Lehmann<\/li>\n<li>Testing Statistical Hypotheses, by E.L.Lehmann<\/li>\n<li>Linear Regression Analysis, by Seber and Lee<\/li>\n<\/ul>\n<p><strong>Notes: &#8211;<\/strong><\/p>\n<ul>\n<li><a href=\"http:\/\/almaak.usc.edu\/~larry\/courses\/Ma541a\/sup\/order-stat.pdf\">Notes on Order Statistics<\/a><\/li>\n<li><a href=\"http:\/\/www.ams.org\/journals\/bull\/1948-54-01\/S0002-9904-1948-08936-4\/S0002-9904-1948-08936-4.pdf\">Wilks on Order Statistics, Bull. Amer. Math. Soc. 54 (1948), 6-50<\/a><\/li>\n<li><a href=\"http:\/\/almaak.usc.edu\/~larry\/courses\/Ma541a\/sup\/method%20of%20moments.pdf\">Method of Moments<\/a><\/li>\n<li><a href=\"http:\/\/almaak.usc.edu\/~larry\/courses\/Ma541a\/sup\/estimating%20equation%20asymptotics.pdf\">Estimating Equation Asymptotics<\/a><\/li>\n<li><a href=\"http:\/\/www.datavis.ca\/courses\/grcat\/grc1.html\">Deaths by horse and mule kicks in the Prussian Army<\/a><\/li>\n<li><a href=\"http:\/\/projecteuclid.org\/DPubS\/Repository\/1.0\/Disseminate?handle=euclid.ss\/1207580174&amp;view=body&amp;content-type=pdfview_1\">The Epic Story of Maximum Likelihood<\/a><\/li>\n<\/ul>\n<p><strong>Computationally Intensive Techniques:<\/strong><\/p>\n<ul>\n<li>Finite Markov Chains and Algorithmic Application. Olle H\u00e4ggstr\u00f6m<\/li>\n<li>The EM Algorithm and Extensions. McLachlan and Krishnan<\/li>\n<li>The Jackknife, the Bootstrap and Other Resampling Plans. Bradley Efron<\/li>\n<\/ul>\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-247","page","type-page","status-publish","hentry"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.0 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Math 541a - Introduction to Mathematical Statistics - Spring 2013 - 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-541a-introduction-to-mathematical-statistics-spring-2013\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Math 541a - Introduction to Mathematical Statistics - Spring 2013 - Larry Goldstein\" \/>\n<meta property=\"og:url\" content=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/math-541a-introduction-to-mathematical-statistics-spring-2013\/\" \/>\n<meta property=\"og:site_name\" content=\"Larry Goldstein\" \/>\n<meta property=\"article:modified_time\" content=\"2023-06-20T19:56:45+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-541a-introduction-to-mathematical-statistics-spring-2013\\\/\",\"url\":\"https:\\\/\\\/dornsife.usc.edu\\\/larry-goldstein\\\/math-541a-introduction-to-mathematical-statistics-spring-2013\\\/\",\"name\":\"Math 541a - Introduction to Mathematical Statistics - Spring 2013 - Larry Goldstein\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/dornsife.usc.edu\\\/larry-goldstein\\\/#website\"},\"datePublished\":\"2023-06-13T19:58:31+00:00\",\"dateModified\":\"2023-06-20T19:56:45+00:00\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/dornsife.usc.edu\\\/larry-goldstein\\\/math-541a-introduction-to-mathematical-statistics-spring-2013\\\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/dornsife.usc.edu\\\/larry-goldstein\\\/math-541a-introduction-to-mathematical-statistics-spring-2013\\\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/dornsife.usc.edu\\\/larry-goldstein\\\/math-541a-introduction-to-mathematical-statistics-spring-2013\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\\\/\\\/dornsife.usc.edu\\\/larry-goldstein\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Math 541a &#8211; 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