85237 - Nonparametric Statistics

Learning outcomes

By the end of the course the student knows the fundamentals of the most relevant nonparametric techniques for statistical inference. In particular, the student is able to solve hypothesis testing problems where the conditions for the traditional parametric inferential tools to be applied are not fulfilled; to build nonparametric density estimators or nonparametric estimators of the regression function; and to use these methods in an effective and coherent way.

Course contents

Introduction.
Hypothesis testing about the probability of an event, on a single sample, on two paired samples and on two independent samples; the case of more than two (dependent/independent) samples.
Hypothesis testing about a location measure, on one sample, on two paired samples and on two independent samples.
One-way and two-way analysis of variance by ranks.
Goodness-of-fit tests.
Measures of association and related hypothesis testing methods.
Nonparametric methods for probability density function estimation: histogram, naive, kernel, nearest neighbour estimators.
Nonparametric methods for regression function estimation: kernel smoother; loess.
Nonparametric methods for statistical learning.

 

For the topics introduced by the lecturer, tutorial applications will be carried out in computer laboratory using R software.

Readings/Bibliography

Beyond teaching material provided by the lecturers (and available at http://campus.unibo.it/) the following references are recommended as additional readings:

• M. Hollander, A. W. Douglas, E. Chicken, Nonparametric statistical methods, Wiley, New York, 2014.
  ISBN: 978-0-470-38737-5.

• Scott, David W. Multivariate density estimation: theory, practice, and visualization. John Wiley & Sons, 2015.

• T. Hastie, R. Tibshirani, and J. Friedman (2001) The Elements of Statistical Learning: data mining, inference and prediction. Springer Verlag.
  Freely available at: https://web.stanford.edu/~hastie/Papers/ESLII.pdf

Teaching methods

Lectures. Tutorial applications in class and in computer laboratory.

Assessment methods

The exam aims to test the student's achievement of the following purposes:

• deep knowledge of the theoretical methods described and discussed;
• critical skill in choosing the most adequate inferential tool to solve a given problem and ability to interpret the corresponding results.

The exam consists of a mandatory written exam (110 minutes). Oral exam is on demand.

The written exam consists of exercises, some of which can be solved by using R software, and theoretical questions. During the exam, using lecture notes, books or electronic devices is forbidden. 

The overall evaluation is expressed in marks out of 30. Having the oral exam, the evaluation obtained in the written exam can change by plus or minus 3 marks at most.

Teaching tools

Blackboard; PC; videoprojector; computer laboratory
Teaching material is available at http://iol.unibo.it/ (download is only allowed to the students that have the course in their study plan)

Office hours

See the website of Laura Anderlucci