The Department of Statistics offers the following courses over the whole academic year:

 

FALL SEMESTER

 

1. Applied Linear Models (Reading Course)

V. Vasdekis           

8 ECTS credits

Course Content

Linear models definition, examples, least squares solution using matrices, ML solution, Hypothesis testing, the general linear hypothesis, F criterion, distributions of quadratic forms, ANOVA of linear models and goodness-of-fit, choice of models, residuals and diagnostic graphs, transformations of dependent and independent variables, sensitivity analysis, hat matrix, influential points, multicollinearity, parameterization of ANOVA models, contrasts, non-balanced models.

Bibliography

·         Montgomery, Peck and Vining (2001). Introduction to linear regression analysis, Wiley

·         Ryan (1997). Modern regression methods, Wiley.

·         Atkinson (1985). Plots, transformations and regression, Oxford university Press

·         Cook and Weisberg (1982). Residuals and Influence in regression, Chapman and Hall

2. Computational Statistics (Reading Course)

D. Karlis

8 ECTS credits

The course has the following parts

·         Kernel density estimation

·         Randomizations tests

·         Monte Carlo tests

·         Jackknife and Cross Validation

·         Bootstrap methods

The course shows  how we can proceed to statistical inference making use of computing. During the course there are 3-4 projects. The projects need computing in R. Special functions to do so are supplied.

 

3. Stochastic Models and Simulations (Reading Course)

P. Dellaportas

8 ECTS credits

Course Content

The course is concerned with a series of simulation techniques. First, algorithms for simulation from random variables including inversion method and rejection algorithm are studied. Then, Monte Carlo techniques including importance sampling and variance reduction strategies are of interest. In the last part of this course Markov chain Monte Carlo simulation algorithms are discussed and modern variance reduction strategies are studied.

 

4. Multivariate Statistical Techniques (Reading Course)

I. Ntzoufras & D. Karlis

8 ECTS credits

The course has the following parts

·         Cluster anlaysis (hierarchcial, K-means , model based clustering)

·         Correspondence analysis and MCA

·         Discriminant analysis and related methods (k-nn and other classification methods)

During the course there are 3-4 projects. The projects need computing in R.

 

5. Introduction to Mathematical Analysis (Reading Course)

Ath. Giannakopoulos

8 ECTS credits

Course Content

This is an introduction to real analysis as opposed to calculus. Its aim is to familiarize the student with the concepts of real analysis so as to be able to proceed to advanced courses in probability, statistics, optimization, mathematical economics, finance etc.

The syllabus is as follows:

1. Sequences and series

2. Continuous and convex functions

3. The Stieltjes integral

4. Introduction to Metric spaces

5. Inner product spaces

 

6. Stochastic Finance (Reading Course)

Ath. Giannakopoulos

8 ECTS credits

Course Content

This is an introduction to the modern theory of stochastic finance. The aim of the course is to introduce the students to the basic concepts of this field, which are to be used in asset pricing, portfolio optimization etc.

The syllabus is as follows:

1. Introduction, assets and assets markets

2. Arbitrage and the pricing kernel

3. Stochastic models for stocks

4. Derivative pricing, the binomial and the Black – Scholes model – martingale pricing and the equivalent martingale measure

5. Introduction to bond pricing

6. Introduction to portfolio theory

 

7. Econometrics

(A. Livada)

8 ECTS credits

Course Content

·         Introduction

·         Hypotheses and properties for the classical model

·         LS method, Indirect LS

·         ML method

·         2sls, 3sls, FIML,

·         Instrumental Variables

·         Violations

·         Autocorrelation

·         Heteroscedasticity

·         Multicollinearity

·         Multipliers

·         Identification problem

·         Dummy variables

 

8. Sampling techniques and sample surveys (Reading Course)

I. Papageorgiou

8 ECTS credits

Course Content

Introduction to Sampling Theory. Population, census, sample, sampling techniques, characteristic under study. Population parameters of interest. Simple Random Sampling (SRS). Estimates of population mean, total, proportion, ratio and proportion. Confidence intervals. Minimum sampling size. Stratified sampling (ST). Description, Estimation, comparison with SRS. Systematic Sampling (SY). Description, Estimation, comparison with SRS and ST. Cluster sampling. Description. One stage, two stages and generalization. Estimation and comparison with other sampling techniques. Multi-stage sampling. Errors in sampling surveys. Questionnaire.

Bibliography

·         Cochran W.G. (1977). Sampling Techniques. Third Edition. John Wiley &Sons. New York.

·         Sampling Methodologies with Applications (2000) Poduri S.R.S. Rao, Chapman and Hall.

·         Kish, L. (1965). Sampling Surveys. John Wiley & Sons. New York.

·         Barnett, V. (1974). Elements of Sampling Theory. The English Universities Press Ltd.

·         Pascal Ardilly, Yves Tillé. Sampling Methods: Exercises and Solutions.

 

9. Actuarial Mathematics of Accident Insurance (Reading Course)

A. Zimbidis

8 ECTS credits

Course Content

Uncertainty, Risk, Insurance, Insurance Companies, Actuaries, Insurance Concepts, Products, Actuarial base

Frequency, severity and pricing methodology premium adjustments, Projections and trends for the final payments by using linear and other models, Reserving methods, Analysis of Insurance Data, Triangular methods and olistic methods of reserving, Discounting reserves, and Confidence Intervals

Reinsurance schemes, «Bonus-Malus» and Markov Chains.

 

10. Risk Theory (Reading Course)

A. Zimbidis

8 ECTS credits

Course Content

 'Risk' and pricing principles, theory of utility of money (Utility Theory), and premium calculations. Description and foundation of the Individual Model, Distribution of the aggregate claims S, safety loading.

Description and foundation of the Collective Model, Compound distributions (Binomial, Poisson and negative binomial) and their properties and joint distributions and their applications, the standard approach of the individual from the collective model

Extension of the collective model beyond a certain period, the surplus process (in discrete and continuous time), probability of ruin, Definition of the functions υ(u) and δ(u), adjustment coefficient R, Probability of ruin for the compound Poisson

Practical applications to insurance problems. Reinsurance Schemes.

 

 

SPRING SEMESTER

 

1. Bayesian Statistics (Reading Course)

P. Dellaportas

8 ECTS credits

Course Content

Objective and subjective probability, interpretation of the Bayes rule, inference based on the Bayesian rule, conjugate priors and non informative distributions, point estimation and confidence intervals, predictions, tests on simple and multiple hypotheses, Lindley‘s paradox, linear regression, model selection, sequential hypothesis testing, Wald‘s identity (equation), expected value of random sample size.

 

2. Biostatistics & Epidimiology (Reading Course)

I. Ntzoufras

8 ECTS credits

Proposed Bibliography in Greek

·         Ntzoufras, I. (2006). Introduction on Epidemiology and Biostatistics. University course notes, Department of Statistics, Athens University of Economics and Business, Greece

·         Pagano M. και Gauvreau, Κ. (2000). Αρχές Βιοιατρικής. (μτφ. Ρ.Δαφνή)

·        Τριχόπουλος, Δ. (1982). Επιδημιολογία: Αρχές, Μέθοδοι και Εφαρμογές.

·         Τριχόπουλος, Γ. (2002). Γενική και κλινική επιδημιολογία: εγχειρίδιο επιδημιολογίας και αρχών κλινικής έρευνας.

·         Corresponding English Textbooks of Proposed Bibliography in Greek

·         Pagano M. and Gauvreau, Κ. (2000). Principles of Biostatistics. 2nd edition. Duxbury Press.

·         McMahon, B.M.D. and Trichopoulos, D. (1996). Epidemiology: Principles and Methods. 2nd edition, Lippincott Williams & Wilkins.

Proposed English Bibliography

·         Rosner, B. (2006). Fundamentals of Biostatistics. 6th Edition. Duxbury Press. [3]

·         Armitage, P., Berry, G. and Mathews JNS (2002). Statistical Methods in Medical Research. 4th Edition. Blackwell Science. [3]

·         Armitage, P. and Berry, G. (1994). Statistical Methods in Medical Research. 3rd Edition. Blackwell Science. [6]

·         Daly, LE, Bourke, GJ, McGilvray, J (1991). Interpretation and Uses of Medical Statistics. 4th Edition. Blackwell Science. [1]

·         Pereira – Maxwell, F. (1998). A-Z of Medical Statistics. Arnold Publications. [4]

·         Everitt, B and Rabe-Hesketh S. (2001). Analyzing medical data using S-PLUS. New York:Springer. [2].

·         Altman, G. (1991). Practical Statistics for Medical Research. Chapman & Hall, Great Britain.[1]

Additional Proposed English Bibliograph (Special topics of Biostatistics)

1. Reference:

·         Armitage, P. and Colton, T. (1998). Encyclopedia of biostatistics. Willey. [8 volumes – ΔΦ]

2. Clinical Trials:

·         Pocock SJ (1983). Clinical Trials: A practical Approach. Willey. [1]

·         Schlesselman, JJ (1982). Case – Controls Studies: Design, Conduct, Analysis. Monographs in Epidemiology and Biostatistics. Oxford University Press. [1]

·         Friedman, LM, Furberg, CD and DeMets DL (1998). Fundamentals of Clinical Trials. 3rd Edition. Springer. [1]

3. Survival Analysis:

·         Yamagichi, K. (1991). Event History Analysis. Applied Social Research Methods Series 28, Sage Publications. [1]

·         Cox, D.R. and Oakes, D. (1984). Analysis of Survival Data. Monographs on Statistics and Applied Probability 21, Chapmand and Hall. [6 ΚΓ – 3 ΓΜΜ]

4. Genetics:

·         Sham, P. (1998). Statistics in Human Genetics. Arnold Publications.

·         Elandt – Johnson R.C. (1971). Probability Models and Statistical Methods in Genetics. Willey and Sons. [3]

5. Psychometrics:

·         Everitt, BS. (1996). Making Sense of Statistics in Psychology. Oxford University Press. [2]

·         Dunn, G. (2000). Statistics in Psychiatry. Arnold Publications.

[#] NUMBER OF AVAILABLE COPIES [4/4/2008]

ΚΓ = NORMAL BORROWING

ΓΜΜ = SHORT BORROWING

ΔΦ = LOCAL USE ONLY

 

3. Multivariate statistical analysis (Reading Course)

D. Karlis

8 ECTS credits

The course has the following parts

·         Multivariate descriptive and graphs

·         Multivariate normal and related distributions

·         Hypotheses tests for multivariate data

·         MANOVA

·         Multivariate Linear model

·         Principal Components Analysis

·         Factor Analysis

During the course there are 3-4 projects. The projects need computing in R.

 

4. Introduction to measure theory & integration with applications to probabilty theory (Reading Course)

Ath. Giannakopoulos

8 ECTS credits

Course Content

This is an introduction to measure theory that will allow students to follow the advanced courses in probability theory, stochastic processes etc as well as applications to statistics or mathematical finance.

The syllabus is as follows

1.       Discrete measures

2.       Lebesgue measure, construction and properties

3.       Lebesgue integration

4.       Convergence theorems for the Lebesgue integral

5.       Introduction to Lebesgue spaces

6.       Hilbert spaces and the projection theorem – Applications in probability

7.       Radon-Nikodym derivatives of measures – Applications in probability

 

5. Index numbers theory and official statistics

A. Livada

8 ECTS credits

Course Content

·         Definitions.

·         Simple and Composite Indices.

·         Choice of goods and services.

·         Wheights.

·         Arithmetic, Geometric, Harmonic Mean Indices.

·         Laspeyres‘ Index, Paasche‘s Index, Marshall-Edgeworth Index, Fisher Index. Criteria of choice.

·         Applications (Consumer Price Index etc)

 

6. Theoritical Statistics (Reading Course)

I. Papageorgiou

8 ECTS credits

The course is an advanced course in Mathematical Statistics.

Topics that will be covered:

1.       Point estimation. Methods of evaluating the estimates. Bias, minimum mean square error, sufficiency, completeness, consistency, efficiency. Methods of finding the estimates. Methods of moments, Maximum Likelihood. Fisher‘s information, Cramer-Rao lower bound, exponential family, Rao-Blackwell and Lehmann-Scheffee theorems.

2.       Confidence Intervals (CI). Construction of confidence interval. Pivotal quantity. Finding a pivotal and construct a CI. Optimum CI. General method of finding a CI. Approximate CI.

3.       Statistical Hypothesis, introduction and terminology. Methods of Evaluating tests. Error probabilities and Power function. Uniformly Most Powerful test (UMP). Neyman-Pearson Lemma for UMP tests. Likelihood Ratio Test (LRT). Asymptotical statistical tests.

Bibliography

·         Casella, A-G. and Berger, R. (1990). Statistical Inference, Wadsworth, Inc., Belmont

·         Freund, J. and Walpole, R. (1980). Mathematical Statistics, 3rd edition, Prentice- Hall, New Jersey

·         Hogg, R. and Graig, A. (1978). Introduction to Mathematical Statistics, 4th edition, Macmillan Company, New York

·         Lehmann, E. L. (1959) Testing Statistical Hypothesis, John Wiley, New York

·         Lehmann, E. L. and Casella, G. (1998) Theory of Point Estimation. 2nd edition

·         Zacks, S. (1970). The Theory of Statistical Inference, John Wiley, New York.

 

7. Actuarial Mathematics of Life Insurance ( Reading Course)

A. Zimbidis

8 ECTS credits

Course Content

Survival function, Simple mortality table and related functions, force of mortality, laws Classics mortality, actuarial tables and commutation functions, Stochastic approach to Life Insurance.

Life annuities with one or more payments annually, Relationship between annuities, life insurance of various kinds, Relationship annuities and insurance, interest rate movements and mortality.

Net premiums and gross premiums, concept and process of calculating reserves, Relationship between successive stock price.

Tables and Actuarial functions for two or more persons, contingent actuarial functions.

 

8. Actuarial Statistics (Reading Course)

A. Zimbidis

8 ECTS credits

Course Content

Measurements of mortality, Form of age specific mortality, mortality comparisons and methods of standardization, life tables and multiple risks. Selection of life tables (Control x2, individual standard deviations, individual absolute standard deviations, cumulative deviations, sign, change sign, steven‘s test) Exposed to risk population (Full-accurate method, the inventory method based on lx) Empirical data smoothing techniques (graphical methods, Parametric models, Moving averages - Smoothing with reference to a typical table epiviosis) Technical spread table survival (Method Lagrange, Parametric model)

 

9. Design and analysis of experiments

V. Vasdekis

8 ECTS credits

Course Content

Basic principles for designing an experiment, comparison between two independent samples, comparison between two dependent samples, experiments with a single factor, parametric and nonparametric approaches, Block randomized experiments, Analysis of covariance. Factorial designs, mixing factorial and blocking experiments. Factorial experiments with random effects, nested and split-plot designs.