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.