Study-Unit Description

Study-Unit Description


CODE SOR2221

 
TITLE Statistical Inference 1

 
LEVEL 02 - Years 2, 3 in Modular Undergraduate Course

 
ECTS CREDITS 6

 
DEPARTMENT Statistics and Operations Research

 
DESCRIPTION 1. General considerations about the nature of statistical inference and a background to the three main theories: frequentist, Fisherian and Bayesian within the context of populations and samples.

2. Families of Models through the parametrization of distributions. Examples of simple parametric models, location – scale models, more complicated families like the exponential family. How the dimensionality of the parameter determines the type of model under consideration.

3. Nonparametric Statistics: the setting – how concerns about lack of knowledge or complexity of underlying distribution as well as violation of common assumptions in standard classical statistical results led to the study of nonparametric statistics. Distributional results about runs, rank and order statistics.

4. Categorical Data: the setting – how the nature of categorical data requires a different type of analysis less dependent on algebra and how the 1960’s heralded a new wave of interest and multiplicity of uses. Results within hypergeometric, Poisson and Multinomial distributional settings as in contingency tables. Overdispersion.

5. Estimators and Statistics, Methods of Estimation: Method of Moments, Least Squares, Maximum Likelihood; description and numerical considerations, Mean Square Error.

6. Properties of Estimators: Unbiasedness, Consistency, Efficiency, Sufficiency, Ancillarity, Nuisance Parameters and Completeness.

7. Likelihood Theory; Cramer-Rao bounds, Fisher information, Likelihood ratio, asymptotic results.

8. The Decision theoretic approach: formulation and risk function, admissible, minimax and randomized decision rules.

9 Hypothesis testing: type I & II errors, Neymann-Pearson theory, power function of a test, uniformly most powerful tests.

10. Goodness-of-fit considerations: Pearson Statistic and Chi-squared test, Kolmogorov-Smirnov and Cramer-von Mises-type Statistics, Lilliefors test.

11. Tests for Categorical Data: Contingency tables, Minimum Chi-Square Method, Relative Risk, Odds Ratio.

12. Bayesian statistics: basic theory including Priors, Posteriors, Bayesian Estimators, and Bayes decision rules.

13. Measures of Association for continuous random variables: correlation and regression.

14. Measure of Association for ordinal and categorical data: rank correlation, contingency table-related statistics, Chi-Square Test for independence, Fisher Exact Test, ordinal measures of association.

15. Statistical Decision Theory: risk functions (utility and loss), properties of good decision rules, Bayes randomized decision rules, finite decision problems, minimax problems, and their corresponding estimators.

16. Goodness of Fit:
- one-way analysis of variance as a simple model for which all the measures of fitness, plus relatively elementary results can be used to talk about MSE, prove the equality SST = SS(Tr) + SSE and discuss the corresponding F-tests as indications of the suitability of model;
- the chi-squared oriented tests with a multinomial setup;
- the von Mises-Cramer statistics tests based on the discrepancy between true distribution function and empirical one;
- Information theoretic criteria - starting from the expectation of the log likelihood rather than the log likelihood itself, next the Kullback-Leiber divergence functions are considered.

Study-unit Aims:

1. To propose statistical inference as being essentially the main activity in statistical analysis with descriptive summarization, estimation and hypothesis testing as its three main branches;
2.To expose students to the mathematical underpinnings of the subject and the relevant tools for future use;
3. To familiarize students with the particular needs of different types of data that have to be catered for through different mathematical structures and techniques;
4. To encourage students to follow current trends and innovations within research activities related to statistical inference both at the theoretical and practical levels.

Learning Outcomes:

1. Knowledge & Understanding
By the end of the study-unit the student will be able to:

1. Distinguish between the nature of different schools of statistical inference within the context of selections from populations;
2. Distinguish between the statistical tools needed for different types of data. while being fully aware of their strengths and limitations;
3. Describe how an integrative approach between different inference type is being attempted mathematically.

2. Skills
By the end of the study-unit the student will be able to:

1. Distinguish between the nature of different schools of statistical inference within the context of selections from populations;
2. Distinguish between the statistical tools needed for different types of data. while being fully aware of their strengths and limitations;
3. Describe how an integrative approach between different inference type is being attempted mathematically.

Main Text/s and any supplementary readings:

Main Texts

- Agresti, A. (2007) An Introduction to Categorical Data Analysis, Wiley-Interscience
- Collet D. (2002) Modelling Binary Data, Chapman and Hill [a ] Davidson .C., (2008) Statistical Models , Cambridge University Press
- Knight K. (1999) Mathematical Statistics, CRC [A] Parmigiani, G. and Inoue, L. Y. T., Decision Theory: Principles and Approaches, Wiley

Supplementary Texts:

- Barnett, V., (1999) Comparative Statistical Inference, Wiley
- Cox, D.R., (2006) Principles of Statistical Inference , Cambridge University Press
- Everitt B.S. (1992) The Analysis of Contingency Tables, Chapman and Hall
- Fienberg S. (2007) The Analysis of Cross-Classified Categorical Data, MIT Press
- Freund, John E. (2003) Mathematical Statistics, Prentice Hall
- Hogg, R.V. and Craig, A.T. (2012 Introduction to Mathematical Statistics, Macmillan
- Longford, N. T., (2013) Statistical Decision Theory , Springer
- Powers D.A., Yu Xie., (2008) Statistical Methods for Categorical Data Analysis, Academic Press
- Rohatgi, V.K. (2003) Statistical Inference, Wiley
- Rohatgi, V.K. (2011) An Introduction to Probability Theory and Mathematical Statistics, Wiley
- Roussas George G. (2013) A Course in Mathematical Statistics, Academic Press
- Sheskin, David J. (2004) Handbook of Parametric and Non-Parametric Statistical Procedures, Chapman and Hall/CRC.

 
ADDITIONAL NOTES Pre-Requisite qualifications: A-Level Maths

Pre-Requisite Study-Units: SOR1110, SOR1220

Co-Requisite Study-Unit: SOR2211

 
STUDY-UNIT TYPE Lecture and Tutorial

 
METHOD OF ASSESSMENT
Assessment Component/s Assessment Due Resit Availability Weighting
Assignment SEM2 No 30%
Examination (3 Hours) SEM2 Yes 70%

 
LECTURER/S Maria Kontorinaki
Fiona Sammut
Lino Sant

 
The University makes every effort to ensure that the published Courses Plans, Programmes of Study and Study-Unit information are complete and up-to-date at the time of publication. The University reserves the right to make changes in case errors are detected after publication.
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Units not attracting a sufficient number of registrations may be withdrawn without notice.
It should be noted that all the information in the description above applies to study-units available during the academic year 2020/1. It may be subject to change in subsequent years.

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