# Advanced Statistics II - Professor Dr. Matei Demetrescu # I. Course description:

The course provides a rigorous foundation in the principles of statistical inference. The course gives a solid and well-balanced introduction to methods of parameter estimation and testing of statistical hypotheses (it even touches on Bayesian inference) in a parametric framework. After completing the course you will understand and will be able to apply the main inferential tools discussed here.

This course is essential for specialization courses in statistics and econometrics (Time Series Analysis, Statistics for Financial Markets, Microeconometrics, Multivariate Statistics, etc.).

# II. Prerequisities:

The course builds on  Adv. Statistics I.

# III. Details:

• Course, 2 hrs. per week.
• Tutorial, 1 hr. per week.
• Written exam, solving problems similar to those discussed in the tutorial.

# IV. Outline:

1. Point Estimation:

1.1  Stochastic Models

1.2  Estimators and Their Properties

1.3  Sucient Statistics

1.4  Minimum Variance Unbiased Estimation

2. Point Estimation Methods:

2.1  The method of Maximum Likelihood

2.2  The (Generalized) Method of Moments

2.3  Bayesian Estimation

3. Hypothesis Testing:

3.1  Fundamental Notation and Terminology

3.2  Parametric Test and Test Properties

3.3  Construction of UMP Tests

3.4  Hypothesis-Testing Methods

4. Model selection

# V. Literature:

This course is based on the following textbooks:

• Mood, A. M., Graybill, F. A. and D.C. Boes (1974, 3rd ed.). Introduction to
the Theory of Statistics
. McGraw-Hill.
• Casella, G. and R. Berger (2002, 2nd ed.). Statistical Inference. Duxbury.
• Mittelhammer, R. C. (1996). Mathematical Statistics for Economics and Busi-
ness
. Springer.

### Further useful textbooks

• Dudewicz, E. J. and S. N. Mishra (1988). Modern Mathematical Statistics. John Wiley & Sons.
• Hogg, R. V. and R. Craig (1995, 5th ed.). Introduction to Mathematical Statistics. Prentice Hall.
• Rohatgi, V. K. und A. K. Saleh (2001, 2nd ed.). An Introduction to Probability Theory and Mathematical Statistics. John Wiley & Sons.