Estimation and non-parametric tests

Non-parametric methods are important in many statistical applications, as they allow us to move away from conventional approaches that require the specification of valid statistical models. Establishing the validity of such a model is a complex undertaking.

Non-parametric methods circumvent this problem by transforming data into ranks and conditioning on certain quantities derived from the observed configuration of these ranks. The statistics thus constructed are independent of the distribution of the raw data, enabling the construction of statistical inference procedures free from the model underlying the data. Moreover, the loss of statistical efficiency is minimal.

This course is a fairly comprehensive presentation of non-parametric methods. It follows on from a first introductory course on parametric inferential methods, adapting and developing the theory of several advanced concepts such as conditional testing, comparative power of tests (efficiency measures) and the notion of "effect size". It focuses on the practical application of these methodologies, with an overview of the main R commands and their uses.

To enable students to understand the limitations of parametric statistical methods, to choose an appropriate non-parametric approach to a given problem based on the underlying statistical principles, to implement the solution to their problem using R software, and to report to end-users on the conclusions of their analyses and their implications.

An M-level inferential statistics course

An L-level probability course
 

 
Recommended prerequisites: An L-level descriptive statistics course

Full continuous assessment

1. Definitions of Nonparametric Statistics
   
   2. Two tricks for removing dependence on an unknown parameter: conditioning (with application to contingency tables, chi-squared tests and Fisher-Yates tests) and rank transformation.
   
   3. The Wilcoxon-Mann-Whitney 2-sample test: Assumptions and test statistics; exact and asymptotic behavior under H0, the case of tied data, test robustness.
   
   4. Variants and extensions of the Wilcoxon-Mann-Whitney test: Point and interval estimation of the effect of treatments, the case of paired samples, power of the Wilcoxon-Mann-Whitney test i) when the Student paradigm holds and ii) when it does not. Notions of "effect-size", calculation of sample sizes to obtain target power.
   
   5. Other tests for the case of 2 samples: Kolmogorov-Smirnov test, Ansari-Bradley test
   
   6. The case of K >2 samples: Kruskal-Wallis test, Friedman-Tukey test. The problem of multiple comparisons. Controlling p-value: Holm's method, FDR (false discovery rate) method
   
   7. Independence, correlation and regression: Pearson's correlation coefficient, Spearman, Kruskal, test of independence. Application to regression
   
   R software implementation of the main non-parametric tests covered in the course.

Timetable:
CM: 15h
TD: 15h
TP:
Field :