Offered by La Trobe University STA4SI Statistical Inference Course Description: This unit covers a selection of topics in classical statistical inference at the fourth year level. It consists of a selection of material from the following chapters of Casella and Berger (2002): Chapter 6 (Principles of Data Reduction), Chapter 7 (Point Estimation), Chapter 8 (Hypothesis Testing), Chapter 9 (Interval Estimation) and Chapter 10 (Asymptotic Evaluations). A knowledge of this material is helpful in almost any statistical endeavour. Reference: Casella, G. and Berger, R.L. (2002) Statistical Inference, 2nd edition. Duxbury. Detailed syllabus: Week 1: Overview of sufficiency and minimal sufficiency. Week 2: Ancillary statistic defined as a statistic whose distribution does not depend on . Alternative definition of ancillary statistic via preliminary reduction by minimal sufficiency. The role of ancillary statistics in inference - Cox's mixture of normal distributions example. Week 3: Review of inference conditional on an ancillary statistic: (a) importance in practice and (b) the requirement of using a conditional distribution cannot be deduced from that of maximum power and that indeed the two requirements may conflict. Data reduction by invariance. Week 4: Revision of the method of moments and maximum likelihood estimation from third year statistical inference. Introduction to two methods of evaluating estimators - (a) comparison after first restricting the class of estimators (e.g. to be unbiased) and (b) comparing the risk functions. Week 5: Review of the Cramer-Rao inequality. Proof of this inequality. Week 6: Introduction to the likelihood ratio test. Also, an introduction to Intersection-Union tests. Week 7: Proof of the Neyman-Pearson lemma. Level and size of Intersection-Union tests. Week 8: p-values from an advanced standpoint (Probability Integral Transform result assumed), including in the presence of nuisance parameters. Confidence sets obtained by inverting hypothesis tests. Week 9: Convergence in probability and convergence in distribution. Week 10: Slutsky's theorem, the Delta Method, the definition of a consistent estimator and the difference between limiting and asymptotic variances. Week 11: Introduction to asymptotic optimality of the maximum likelihood estimator. Week 12: Some details of the proof of asymptotic optimality of the maximum likelihood estimator. Examples of approximate maximum likelihood intervals. Lecturer Contact Details: Name: Associate Professor Paul Kabaila Phone: 3 9479 2594 Email: P.Kabaila@latrobe.edu.au Homepage: http://www.latrobe.edu.au/mathstats/staff/kabaila.html Start date: 27 July 2009 End date: 30 October 2009 Excluding the week: 17 -21 August 2009 Number of teaching weeks: 12 Contact hours per week: 2 hours of lectures (Mondays 10-12) + half an hour for homework assistance across Access Grid Offered by the University of Wollongong STAT 904/401 Statistical Consulting Subject Coordinator: Prof David Steel (Room 15.G17) Email: dsteel@uow.edu.au Phone: (02) 4221 3823 Consultation: Tues 2.00pm-4.00pm or by appointment Assumed Knowledge: Major in undergraduate statistics. Consultation: Tues 2.00pm-4.00pm Topics, Outline & Lecturers: In this subject we consider the issues associated with the role of statistical consultant and client. Topics include: communication skills, choosing analysis techniques, developing appropriate study designs, questionnaire development and piloting, researching the unknown, sample size, initial interviews, follow-up interviews reporting, and time management Guest lecturers will also be used. Textbook & Reference Books: Students are not required to purchase reference books. Rather you will be expected to conduct literature reviews to identify current resources and issues in consulting using the Library catalogue and databases. Various background reading materials will be made available to you. Notices: Students should check their email frequently as all communication, notices, and changes will be emailed to students. Any student who has difficulty with email should contact the lecturer of the subject to make alternative arrangement for notices. Graduate Qualities: The University of Wollongong is committed to developing graduates with qualities that will equip them for roles in society and the workplace. Refer to the full Graduate Qualities inventory at http://www.uow.edu.au/about/teaching/qualities/ Students will acquire the following graduate qualities as a result of their participation in this subject: 1.) Informed- a) Have sound technical knowledge in mathematics and/or statistics at a level to enable informed contribution in the community b) Understand the applications of mathematics and/or statistics to other fields. c) Be aware of the breadth of the discipline(s) of mathematics and /or statistics. 2) Independent Learners- a) Have skills in accessing, understanding, summarising, extending and generalizing technical information b) Have the ability to work independently. c) Be able to demonstrate a facility with technical computer software that enhances their expertise in mathematics and/or statistics. d) Understand conventions for the referencing, citation and attribution of the work of others. 3) Problem Solvers- a) Be capable of applying logical, analytic and creative thinking to a range of problems. b) Display skills in constructing clear, precise and rigorous mathematical and/or statistical arguments as well as critical thought and analysis in the practice of mathematics and/or statistics. c) Are able to identify and apply relevant mathematical and/or statistical techniques to a problem; adapting or extending them as necessary. 4) Effective Communicators- a) Be able to communicate effectively on mathematical and/or statistical issues at technical and lay level and in both oral and written form. b) Be able to interpret data and results from mathematical and/or statistical analysis and draw valid conclusions. 5) Responsible- Be aware of and able to develop arguments about limitations and ethical and privacy issues, in the design, analysis and written reports of mathematical and/or statistical models and studies. Subject Learning Outcomes: After successful completion of this subject, students should be able to perform the following tasks which develop the listed Graduate Qualities (GQ): (i) Identify and deal with ethical issues arising through the consulting relationship (ii) Conduct an initial interview as a statistical consultant, eliciting the problem and directing appropriate follow-up. (iii) Appraise statistical consulting sessions conducted by others. (iv) Analyse and report to a client in a timely and effective manner. (v) Research topics previously unknown to them (vi) Identify relevant analysis and design approaches in practical situations. {GQ: 1(a),(b),(c), 2 (a),(b),(c),(d), 3 (a),(b),(c), 4 (a),(b),(c). 5 ] Lectures & Tutorials:There is one two-hour class scheduled each week for Monday 9.30am - 11.30am in 15.113 (Access Grid Room), which will be used for lectures and tutorials. You are required to attend all lectures in STAT904. Experience has shown that poor attendance at lectures leads to poor performance in this subject. Attendance will be monitored at each lecture. To get the most from this subject you should actively participate in discussions in the lectures, but your participation will not be assessed. A student of average ability would be expected to work 12 hours per week in the subject to achieve an average result. A student who is below average in ability or wishes to achieve an above average result should expect to work more than12 hours per week. This figure of 12 hours includes the hours taken up with formal classes. Assessment: Your final mark in STAT904 will be determined as follows*: Weekly Assignments (9) -54% Consultant Observations -16% Report and Presentation - 20% Summary of important points - 10% Total - 100% *Attendance at classes may be taken into account. Scaling of marks is not a standard procedure in this subject. Note that you are not required to "pass" each individual component to receive a Pass grade in STAT904. However, you would seriously jeopardize your chances of passing this subject if you do not aim to be successful in every component of the assessment. Final Examination: There is no final examination. Consultation: If you are having difficulty with STAT904, you are encouraged to seek advice from your lecturers or the subject coordinator. For administrative matters, you should see the subject coordinator. If you cannot come at the listed consultation times, contact the subject coordinator to arrange an appointment at a mutually convenient time. When you send an email to a lecturer or the subject co-ordinator, you should do so from your University email account. Email sent from other accounts may be automatically redirected into a junk-mail folder; the staff member may then not read it for several days, or it may be automatically deleted before it is read at all. Furthermore, the subject line of your email should refer to STAT904. For the full list of subjects offered by all Universities over the Access Grid click here |