COURSE UNIT TITLE

: ADVANCED STATISTICAL INFERENCE - I

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
STA 6001 ADVANCED STATISTICAL INFERENCE - I ELECTIVE 3 0 0 8

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

ASSOCIATE PROFESSOR AYLIN ALIN

Offered to

Statistics
STATISTICS

Course Objective

To teach the fundemental theory of statistical inference.

Learning Outcomes of the Course Unit

1   Understanding generating functions
2   Understanding generating functions
3   Understanding the large sample theory of convergence
4   Understanding the main principles of data reduction
5   Obtaining point estimators of a parametre
6   Understanding the propoperties of efficient estimation

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Some basic properties of probability theory , Generating functions: Moment, Cumulant, Characteristic functions
2 Differentiation under Integral Sign
3 Common families of Distributions: Exponential families of distributions, Location and Scale Scale families of Distributions , Inequality and Identities
4 Multiple Conditional Expectation and variance identities for two random variables, Multivariate Distributions,Preparing Individual Assignments
5 Numerical inequalities, Functional inequalities
6 Basic concepts of random sample, sums of random variables from a random sample, properties of sample mean and variance
7 Modes of Convergence, convergence in distribution
8 Limit theorems of sum of independent random variables,Preparing Individual Assignments
9 Limit theorems of sum of independent random variables
10 CLT for Dependent sequences
11 The sufficiency principle, The minimal sufficient statistics, Anciallary statistics
12 The likelihood principle, The equivariance principle,Preparing Individual Assignments
13 Methods of point estimation: The least squares estimation, MLE
14 Cramer-Rao bound for parametric models, Information bound and efficient influence function ;Asymptotic efficiency bounds: Le Cam s Lemma

Recomended or Required Reading

Textbook:
George Casella and Roger L. Berger, Statistical Inference, 2nd edition ,2002, Duxbury
Anirban Das Gupta, Asymptotic Theory of statistics and Probability , 2008 Springer
E.L. Lehman and George Casella, Theory of Point Estimation, 2nd edition , 1998, Springer

Planned Learning Activities and Teaching Methods

Lecture and Homeworks

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 ASG 1 ASSIGNMENT 1
2 ASG 2 ASSIGNMENT 2
3 ASG 3 ASSIGNMENT 3
4 FIN FINAL EXAM
5 FCG FINAL COURSE GRADE ASG 1 + ASG 2 + ASG 3/3 * 0.40 + FIN * 0.60
6 RST RESIT
7 FCGR FINAL COURSE GRADE (RESIT) ASG 1 + ASG 2 + ASG 3/3 * 0.40 + RST * 0.60

Further Notes About Assessment Methods

None

Assessment Criteria

Evaluation of homework assignments and final exam.

Language of Instruction

English

Course Policies and Rules

Attendance to at least 70% for the lectures is an essential requirement of this course and is the responsibility of the student. It is necessary that attendance to the lecture and homework delivery must be on time. Any unethical behavior that occurs either in presentations or in exams will be dealt with as outlined in school policy. You can find the undergraduate policy at http://web.deu.edu.tr/fen

Contact Details for the Lecturer(s)

DEU Fen Fakültesi Istatistik Bölümü
e-mail: aylin.alin @deu.edu.tr
Tel: 0232 301 85 72

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 14 3 42
Preparation for final exam 1 36 36
Preparations before/after weekly lectures 14 3 42
Preparing assignments 3 22 66
Final 1 2 2
TOTAL WORKLOAD (hours) 188

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10
LO.1555
LO.2555
LO.3555
LO.4555
LO.5555
LO.6555

CONTACT INFORMATION
Dokuz Eylül Üniversitesi Cumhuriyet Bulvarı No: 144 35210 Alsancak / İZMİR
Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

Copyright 2012 DEÜ. BİD

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