Non Parametric Statistics (ΣΕΕ14)

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General

School	School of Science
Academic Unit	Department of Mathematics
Level of Studies	Graduate
Course Code	ΣΣΕ14
Semester	2
Course Title	Non Parametric Statistics
Independent Teaching Activities	Lectures-Laboratory (Weekly Teaching Hours: 3, Credits: 7.5)
Course Type	Specialized general knowledge
Prerequisite Courses	-
Language of Instruction and Examinations	Greek
Is the Course Offered to Erasmus Students	Yes (in English, reading Course)
Course Website (URL)	See eCourse, the Learning Management System maintained by the University of Ioannina.

Learning Outcomes

Learning outcomes

This course aims at introducing nonparametric techniques in statistical analysis and the use of these techniques in a variety of disciplines. The course will focus on the so-called smoothing procedures for curve estimation. Students taking this course will develop an appreciation of nonparametric statistics and will be able to: understand the concept and scope of nonparametric techniques, explain the fundamental principles of smoothing and nonparametric curve estimation, estimate functions of interest without strong parametric assumptions, test hypotheses about these functions and construct confidence regions, use in practice the modern nonparametric techniques to answer concrete questions about real data sets, use the R software to generate output in regard to the previous point and for computing intensive methods such as the bootstrap.

General Competences

Working independently Decision-making Production of free, creative and inductive thinking Criticism and self-criticism

Syllabus

Presentation and Introduction to nonparametric methods. Nonparametric estimation of the probability density function (p.d.f.) by histogram and by kernel density estimation. Asymptotic properties of the derived estimates. Non parametric estimation of the cumulative distribution function (e.c.d.f.) with the empirical c.d.f., kernel smoothing and properties of the derived estimatres. Methods and techniques for bandwidth selection. Improvements of kernel estimates: elimination of boundary bias, variable bandwidth kernel estimates and transformation-based estimates. Nonparametric regression: the Nadaraya-Watson estimate and the local polynomial estimate. Multivariate kernel estimation and special topics.

Teaching and Learning Methods - Evaluation

Delivery	Classroom (face-to-face)
Use of Information and Communications Technology	Statistical software Use of ICT in communication with students
Teaching Methods	Activity Semester Workload Lectures 39 Working independently 78 Exercises-Homework 70.5 Course total 187.5
Student Performance Evaluation	Final written exam in Greek (in case of Erasmus students in English).

Attached Bibliography

• Silverman, B. (1986). Density Estimation for Statistics and Data Analysis, Chapman and Hall.
• Wand, M.P. and Jones, M.C. (1994). Kernel smoothing, First Edition, Chapman and Hall.
• Simonoff, J.S. (1996). Smoothing Methods in Statistics, Springer.
• Fan, J. and Gijbels, I. (1996). Local Polynomial Modelling and Its Applications, Chapman and Hall.
• Loader, C. (1999). Local Regression and Likelihood, Springer.
• Scott, D. (2015). Multivariate Density Estimation: Theory, Practice, and Visualization, Second edition, Wiley.
• Takezawa, K. (2006). Introduction to Nonparametric Regression, Wiley.
• Wasserman, L. (2006). All of Nonparametric Statistics, Springer.
• Klemela, J. (2009). Smoothing of Multivariate Data: Density Estimation and Visualization, Wiley.
• Tsybakov, A.B. (2009). Introduction to Nonparametric Estimation Springer.
• Chacón, J.E. and Duong, T. (2018). Multivariate Kernel Smoothing and its Applications, Taylor and Francis.
• [Περιοδικό / Journal] Journal of Nonparametric Statistics.