These are the notes I took for a Master's course Nonparametric Methods. The recommended textbook is Applied Nonparametric Statistical Methods, Fourth Edition by Sprent, P. and Smeeton, N.C. (2007).
Basic Concepts
A brief introduction to what we're going to discuss in later chapters.
Jan 25, 2019
Statistics
Visualization
Fundamentals of Nonparametric Methods
Some basic tools such as the permutation test and the binomial test. We also introduce order statistics and ranks, which will come in handy in later chapters.
Feb 1, 2019
Statistics
Permutation
p-value
Location Inference for Single Samples
The Wilcoxin signed rank test explained.
Mar 26, 2019
Statistics
R
Wilcoxon
Asymptotic
Other Single Sample Inferences
Explore whether the sample is consistent with a specified distribution at the population level. Kolmogorov's test, Lilliefors test and Shapiro-Wilk test are introduced, as well as tests for runs or trends.
Apr 26, 2019
Statistics
Visualization
R
Distribution
Asymptotic
Methods for Paired Samples
An obvious extension of the one-sample procedures. We discuss applying the Wilcoxon signed rank test on paired samples. We also introduce the McNemar’s test, which is more or less the same as a sign test.
Apr 29, 2019
Statistics
Wilcoxon
Asymptotic
Two Independent Samples
With two independent samples, we may ask about the centrality of the population distribution and see if there's a shift. Wilcoxon-Mann-Whitney is here!
May 2, 2019
Statistics
Visualization
R
Wilcoxon
Asymptotic
Basic Tests for Three or More Samples
Nonparametric analogues of the one-way classification ANOVA and the simplest two-way classifications, namely the Kruskal-Wallis test, the Jonckheere-Terpstra test, and the Friedman test.
May 4, 2019
Statistics
Visualization
R
Wilcoxon
Asymptotic
Correlation and Concordance
Measures for the strength of relationships between variables (two or more). The Spearman rank correlation coefficient, Kendall's tau and Kendall's W are introduced.
May 5, 2019
Statistics
Categorical Data
Dealing with contingency tables. Fisher's exact test comes back, together with Chi-squared test and likelihood-ratio test. We also talk about testing goodness-of-fit.
May 6, 2019
Statistics
Bootstrap
The procedure and applications of the nonparametric bootstrap. We also discuss the Jackknife estimator.
May 13, 2019
Statistics
R
Distribution
Regression
Density Estimation
Wanna know more about histograms and density plots?
May 17, 2019
Statistics
Visualization
R
Distribution
Modern Nonparametric Regression
LOWESS, penalized least squares and the cubic spline.
May 20, 2019
Statistics
Visualization
R
Regression