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

The course provides a rigorous foundation in the principles of probability and mathematical statistics underlying statistical inference in the field of economics and business. Special emphasis is given to the study of parametric families of distributions, univariate as well as multivariate, and to basic asymptotics for sample averages.

This course is a prerequisite for the lecture Advanced Statistics II, which focuses on the methods of statistical inference including parameter estimation and hypothesis testing.
Furthermore, it provides the foundation for the specialization courses in statistics and econometrics (Time Series Analysis, Statistics for Financial Markets, Microeconometrics, Multivariate Statistics, etc.).

# III. Details:

• Course, 2 hrs. per week.
• Tutorial, 1 hr. per week.
• Written exam, solving problems similar to those discussed in the tutorial.
• You may use a formulary (will be available for download).

# 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.