Mathematical Statistics Chapter 6. Sampling Distribution and Limit Theorems We observe a random sample from a probability distribution of interest and want to estimate its properties. The CLT also comes into place.

Mathematical Statistics Chapter 5. Functions of Random Variables Finding the distribution of a real-valued function of multiple random variables. There's the method of distribution functions, transformations and moment generating functions.

Mathematical Statistics Chapter 4. Multivariate Probability Distributions Joint probability distributions of two or more random variables defined on the same sample space. Also covers independence, conditional expectation and total expectation.

Mathematical Statistics Chapter 3. Continuous Random Variables and Their Probability Distributions PDF, CDF, expectation, variance and MGF of the uniform, normal and exponential distributions. Also two approximations for the binomial distribution.

Mathematical Statistics Chapter 2. Discrete Random Variables and their Probability Distributions PMF, CDF, expectation, variance and MGF of Bernoulli, Binomial, Geometric and Poisson random variables.

Mathematical Statistics Chapter 1. Probability An introduction to the concept of the probability of an event. Set operations, axioms of probability, conditional probability and Bayes' rule.

Nonparametric Methods Modern Nonparametric Statistics (10) The procedure and applications of the nonparametric bootstrap, kernel density estimation, and regression methods such as lowess and the cubic spline.

Nonparametric Methods Categorical Data (9) 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.

Nonparametric Methods Correlation and Concordance (8) 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.

Nonparametric Methods Basic Tests for Three or More Samples (7) 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.

Nonparametric Methods Methods for Two Independent Samples (6) 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!

Nonparametric Methods Methods for Paired Samples (5) Wilcoxon signed-rank test and the sign test (McNemar's test if you prefer) again! The key is to focus on the differences between the paired observations.

Nonparametric Methods Other Single Sample Inferences (4) Explore whether the sample is from a specified distribution (with parameters known or unknown), or if there's any runs or trends in the data.

Nonparametric Methods Location Inference for Single Samples (3) Going deep on the one-sample Wilcoxon signed-rank test. Assumptions, procedure, limitations, implementation in R, and comparison with other methods.

Nonparametric Methods Fundamentals of Nonparametric Methods (2) Some basic tools (permutation test and sign test) and principles (order statistics, ranks, and efficiency).

Nonparametric Methods Some Basic Concepts (1) What is nonparametric statistics? What kind of problems can we solve with it? Here's the starting point for the series Nonparametric Methods.