Nonparametric Statistical Inference

Recommended Prerequisites

Probability, Mathematical Statistics and Stochastic Processes.

Teaching Methods

The classes are essentially of expository style and include examples (using real or simulated data) and exercises to apply the material being taught. 

Learning Outcomes

The main goal of this curricular unit is to give students a first account on nonparametric inference methods. Distribution-free inference and curve smoothing, that are discussed in detail in this curricular unit, are among the broad range of methods for data analysis comprised in modern nonparametric statistics.

This course allows developing the following skills: knowledge of nonparametric statistical models; knowledge of mathematical results; using computational tools.

Work Placement(s)

No

Syllabus

The course intends to explore some topics of  nonparametric inference, with a focus on rank-based and curve smoothing inference. Specific subjects to be studied may include order statistics, empirical functions and goodness-of-fit tests, inference in extreme value models, kernel density and regression function estimation, smoothing parameter selection and estimation of other functions depending on the density.  

Assessment Methods

Assessment 1
Participation in class: 25.0%
Exam: 75.0%

Assessment 2
Participation in class: 25.0%
Synthesis work: 75.0%

Bibliography

J. Beirlant et al., Statistics of Extremes: Theory and Applications, John Wiley & Sons, 2004.

J.D. Gibbons and S. Chakraborti, Nonparametric Statistical Inference, CRC Press, 2010.

J.S. Simonoff, Smoothing Methods in Statistics, Springer, 1996.

M.P. Wand and M.C. Jones, Kernel Smoothing, Chapman and Hall, 1995.

L. Wasserman, All of Nonparametric Statistics, Springer, 2006.