Course Overview: This course is intended for Ph. Math together form a year-long sequence in mathematical statistics leading to the Ph. The first semester will cover introductory measure-theoretic probability, decision theory, notions of optimality, principles of data reduction, and finite sample estimation and inference. We will discuss foundational issues, and consider several paradigms for testing, such as the Neyman-Pearson, neo-Fisherian, and Bayesian approaches.

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Course Overview: This course is intended for Ph. Math together form a year-long sequence in mathematical statistics leading to the Ph. The first semester will cover introductory measure-theoretic probability, decision theory, notions of optimality, principles of data reduction, and finite sample estimation and inference. We will discuss foundational issues, and consider several paradigms for testing, such as the Neyman-Pearson, neo-Fisherian, and Bayesian approaches.

Roughly half of the first semester is devoted to the measure-theoretic foundations of probability theory and statistics. The second semester will cover asymptotic theory, including convergence in measure, limit theorems, integral and density approximations, and higher-order asymptotics.

Maximum likelihood, Bayesian, and bootstrap methods will be considered. Empirical processes, large deviations, and modern topics e. Bayesian nonparametric asymptotics will be introduced as time permits. The style of the course is theorem-proof based; applications will not be emphasized, and examples will be theoretical.

Statistical software is not part of the course. Prerequisite: It is assumed that students have taken a first course in real analysis, probability, and mathematical statistics, and are familiar with basic topology, multivariate calculus, and matrix algebra.

If you are undecided about whether or not to take this course, it may be helpful to look at the Ph. This time there will be more measure theory and probability theory on exams. Textbook: There are many excellent books and online resources for the material in this course. However, no single book is suitable. Due to the cost of purchasing several books, I will not require that students use any particular books. The recommended readings for each lecture are accompanied by sections of three books listed below, but students are welcome to look at other references for the same material.

I will use the same books for Math and Math The links give electronic access to two of the books for Washington University students logged in to library account through SpringerLink, but I also recommend purchasing these books as they are excellent references for researchers.

Athreya and S. Lehmann and G. Young and R. Smith, Cambridge University Press. This book is much shorter and not intended as an encyclopedic reference, but it is perhaps the most clearly-written, insightful treatment of modern statistical inference. Homework: There will be weekly homework assignments. You are strongly encouraged to write your solutions in LaTeX. If not, then handwritten submissions must be clear and organized.

Homework will be graded, but solutions will not be provided to students. Homework grader: Qiyiwen Zhang qiyiwenzhang wustl. Attendance: Attendance is required for all lectures. Homework: There will be regular homework assignments. The lowest homework grade will be dropped. Final Course Grade: The letter grades for the course will be determined according to the following numerical grades on a scale.

Academic integrity: Students are expected to adhere to the University's policy on academic integrity. Auditing: There is an option to audit, but this still involves enrolling in the course. Auditing students will still be expected to attend all lectures and compete all required coursework and exams. A course grade of 75 is required for a successful audit.

Collaboration: Students are encouraged to discuss homework with one another, but each student must submit separate solutions, and these must be the original work of the student. Exam conflicts: Read the University policy. The exam dates for this course are posted before the semester begins, and thus you are expected to be present at all exams. Late homework: Only by prior arrangement. If a valid reason for an exception is not presented at least 36 hours before a homework due date, then it will not be accepted late a zero will be given for that assignment.

Missed exams: There are no make-up exams. For valid excused absences with midterm exams - such as medical, family, transportation and weather-related emergencies - the contribution of that midterm to the final course grade will be redistributed equally to the other midterm exam and final exam. Lazar The ASA's Statements on p-values: context, process, and purpose. American Statistician 70 2 , Walker Why are p-values controversial?

American Statistician , to appear. Alastair Young and R. Smith Barndorff-Nielsen and D. Cox Tom Severini Pace and A. Salvan Principles of Statistical Inference , World Scientific.

Azzalini Lecture 10 Fisherian Principles Part I Distribution constant statistics; sufficiency and likelihood principles. Lecture 11 Fisherian Principles Part II Completeness; conditionality principle; ancillary statistics; parameterization invariance. Suggested reading: Anirban DasGupta, editor Selected Works of Debabrata Basu , Springer. Malay Ghosh Basu's theorem with applications: a personalistic review.

Sankhya A 64 3 , Chapter 3 of Michael Evans Cramer Mathematical Methods of Statistics. Peter McCullagh John Kolassa Series Approximation Methods in Statistics , 3rd edition, Springer.

Lecture 1 Neyman-Pearson testing; optimal simple tests via likelihood ratios; optimal one-sided tests via monotone likelihood ratios Reading: TSH 3. Lecture 4 Optimal unbiased testing with nuisance parameters ; optimal invariant testing Reading: TSH 4.

Lecture 7 Some philosophy of science; interpretations of probability; paradigms of statistical inference; the p-value controversy Reading: TSH 3. Lecture 13 Multivariate Cumulants; Basic Stochastic Convergence Joint cumulants; relationship between moments and cumulants; stochastic convergence definitions and examples References: same as previous lecture.

Lecture 19 Local Linear Approximations Delta method; variance-stabilizing transformations; sampling distributions of order statistics References: Lehmann's book Elements of Large Sample Theory.

April Last day of spring semester classes May 8: Final Exam.

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## Theory of Point Estimation

It seems that you're in Germany. We have a dedicated site for Germany. Authors: Lehmann , Erich L. Since the publication in of Theory of Point Estimation, much new work has made it desirable to bring out a second edition. The greatest change has been the addition to the sparse treatment of Bayesian inference in the first edition.

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