Nonparametric Theory
Explore nonparametric statistical theory through a comprehensive series of lectures covering a wide range of topics. Delve into summation formulas for integers, prove the sign test's power, study derivatives of inverse trigonometric functions, and analyze probability distributions. Examine the Wilcoxon signed rank test, U statistics, and sample variance formulas. Investigate normal scores statistics, empirical CDFs, and probability integral transformations. Learn about Kolmogorov-Smirnov tests, correlation between variate values and ranks, and multivariate sign tests. Discover Spearman's rank correlation, Kendall's tau, and the distribution of sample medians and ranges. Gain practical experience using R for statistical analysis and visualization throughout the course.