{"id":282,"date":"2023-06-13T13:20:59","date_gmt":"2023-06-13T20:20:59","guid":{"rendered":"https:\/\/live-usc-dornsife.pantheonsite.io\/larry-goldstein\/?page_id=282"},"modified":"2023-06-20T13:00:06","modified_gmt":"2023-06-20T20:00:06","slug":"mathematical-statistics-2","status":"publish","type":"page","link":"https:\/\/dornsife.usc.edu\/larry-goldstein\/mathematical-statistics-2\/","title":{"rendered":"Mathematical Statistics"},"content":{"rendered":"\n\n \n \n\n\n\n\n\n\n\n
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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

Review of basic probability and statistics
\nParametric models
\nEstimation: criteria and construction of estimators, maximum likelihood, asymptotics
\nHypothesis testing, multiple hypotheses testing
\nNon parametric models, empirical distribution function, jackknife and bootstrap, non-parametric testing, density and regression estimation
\nClassification: discriminant analysis, support vector machines, multivariate statistics, EM algorithm and simulation including Monte Carlo Markov Chain
\nThe level and detailed content of the course will be determined along with the students according to their background and interests.<\/p>\n

Prerequisite: At least one good course in probability, and some basic statistics.
\nInstructors: Larry Goldstein and Yosi Rinott<\/p>\n

Office Hours: Larry Goldstein, Tuesdays 14:00 – 15:00 and Fridays 15:45-16:45 (before the exercise sessions), room 610.<\/p>\n\n\n\n<\/div>\n\n\n <\/div><\/div>\n\n\n\n\n \n \n\n\n\n\n\n\n\n

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Annoucements<\/strong><\/h3>\n

During the first week of the course we will review probability theory, as covered in the first 5 chapters of our text.<\/p>\n

An additional question, problem and lecture session will be available on Wednesday July 29th from 15:00-16:30 in Aula B3 for students who desire additional exposure to the material that is to be reviewed in week 1.<\/p>\n

An additional class will be held in Aula B3 on Wednesday August 19th at 3:00.<\/p>\n\n\n\n<\/div>\n\n\n <\/div><\/div>\n\n\n\n\n \n \n\n\n\n\n\n\n\n

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Problem Sessions and Exercises<\/h3>\n

Problem session coverage:<\/strong><\/p>\n

Tuesday, July 28th: Chapter 2
\nFriday, July 31st: Chapter 2:11,14,15,16,20, problems from Chapters 3 and 4 as time permits.
\nTuesday, August 4th: Chapters 3 and 4.<\/p>\n\n\n\n<\/div>\n\n\n <\/div><\/div>\n\n\n\n\n \n \n\n\n\n\n\n\n\n

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Exercises:<\/h3>\n

Chapter 2: 4,7,8,11,13a,14,15,16,20,21
\nProve that \u03b1\u0393(\u03b1)=\u0393(\u03b1+1) (three words).
\nProve that the standard normal density integrates to 1 (two words).
\nProve or disprove: If N is an non-negative integer valued random variable, p is any number in [0,1], and X and Y are the number of heads and tails in
\nN independent tosses of a p-coin respectively, then X and Y are independent if and only if N is Poisson.
\nFind the variance of the Poisson and Gamma distributions.
\nShow that the N(\u03bc,\u03c3^2) distribution has mean \u03bc and variance \u03c3^2<\/p>\n

Chapter 3: 1,3,5,7 (ignore hint, use Fubini’s theorem instead), 13 (you may use 17),14,16,17,20,21,23,24
\nChapter 4: 1,2,3,4a,5,6. Also, prove the arithmetic\/geometric mean inequality using Jensen’s inequality.
\nChapter 5: 1,2,4,6,11,12,13,15,16
\nDay1Quiz: problems 1-6<\/p>\n\n\n\n<\/div>\n\n\n <\/div><\/div>\n\n\n\n\n \n \n\n\n\n\n\n\n\n

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Exercise Set 1<\/a>
\nMidterm scores out of 90 possible points: 7,30,37,43,43,44,45,45,65,77,87,90,90,90,90 Median = 45, Average = 59
\nExercise Set 2<\/a>
\nExercise Set 3<\/a>
\nExercise Set 4<\/a>
\nExercise Set 5<\/a>
\nExercise Set 6<\/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\n

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Structure and Evaluation<\/h3>\n

Lectures, Monday through Friday mornings, 8:30-9:30, Problem Sessions Tuesday 15:00-16:30 and Friday 16:45-18:15
\nMidterm, 30% Tuesday August 11th, 14:30-16:30, closed book.
\nFinal Exam, 45% Wednesday August 26th, 15:00-17:00, closed book.
\nCourse participation, 25%
\nCourse Text: All of Statistics: A concise course in Statistical Inference, by Larry Wasserman. <\/p>\n\n\n\n<\/div>\n\n\n <\/div><\/div>\n\n\n\n\n \n \n\n\n\n\n\n\n\n

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Additional References<\/h3>\n

Mathematical Statistics: Basic Ideas and Selected Topics, by Peter Bickel and Kjell Doksum
\nA Course in Large Sample Theory, by Thomas Ferguson<\/p>\n\n\n\n<\/div>\n\n\n <\/div><\/div>\n\n\n\n\n \n \n\n\n\n\n\n\n\n

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Links and Information<\/h3>\n

The Normal Distribution<\/a> in international finance
\nCourse Dinner Photo<\/a>: Tuesday, August 18th
\nClass Photo<\/a>: Exercise Session, Friday, August 21st<\/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-282","page","type-page","status-publish","hentry"],"acf":[],"yoast_head":"\nMathematical 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-2\/\" \/>\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\" content=\"https:\/\/dornsife.usc.edu\/larry-goldstein\/mathematical-statistics-2\/\" \/>\n<meta property=\"og:site_name\" content=\"Larry Goldstein\" \/>\n<meta property=\"article:modified_time\" content=\"2023-06-20T20:00:06+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\/mathematical-statistics-2\/\",\"url\":\"https:\/\/dornsife.usc.edu\/larry-goldstein\/mathematical-statistics-2\/\",\"name\":\"Mathematical Statistics - 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