Nonparametric estimation and testing

Nonparametric methods are important in many statistical applications because they allow us to move away from traditional approaches that require the specification of valid statistical models. However, establishing the validity of such a model is a complex undertaking. 

Nonparametric methods circumvent this problem by transforming the 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, which makes it possible to construct statistical inference procedures that are free of the underlying model of the data. In addition, the loss of statistical efficiency is minimal.
 
This course provides a fairly comprehensive overview of non-parametric methods. It follows on from an introductory course on parametric inferential methods, adapting and developing the theory behind several advanced concepts such as conditional tests, comparative test power (efficiency measures), and the notion of "effect size." It emphasizes the practical application of these methodologies by providing an overview of the main R commands and their uses.

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

A master's-level course in inferential statistics

A bachelor's-level course in probability
 

 
Recommended prerequisites: A descriptive statistics course at the L level

Continuous assessment

1. Definitions of nonparametric statistics
   
   2. Two tricks for removing dependence on an unknown parameter: conditioning (with application to contingency tables, chi-square tests, and Fisher-Yates tests) and rank transformation.
   
   3. The Wilcoxon-Mann-Whitney test for two samples: Test assumptions and 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 Student's paradigm holds and ii) when it does not hold. Concepts of "effect size," calculation of sample sizes to obtain a 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. P-value control: Holm method, FDR (false discovery rate) method
   
   7. Independence, correlation, and regression: Pearson, Spearman, and Kruskal correlation coefficients, independence test. Application to regression
   
   Implementation of the main non-parametric tests covered in the course using R software.

Hours per week:
Lectures: 15 hours
Tutorials: 15 hours
Practical work:
Fieldwork: