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YouTube

Nonparametric Theory

statisticsmatt via YouTube

Overview

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This course covers nonparametric theory and its applications in statistics. The learning outcomes include understanding various nonparametric tests such as the Sign Test and Wilcoxon Signed Rank Test, as well as correlation measures like Spearman's Rank Correlation and Kendall's Tau Rank Correlation. Students will learn to calculate test statistics, variance, and covariance, and apply nonparametric methods using statistical software like R. The course teaches skills in hypothesis testing, rank correlation analysis, and order statistics. The teaching method involves theoretical explanations, mathematical derivations, and practical examples using R. The course is intended for individuals interested in expanding their knowledge of nonparametric statistics and its real-world applications.

Syllabus

Summation Formulas for Integers.
Prove the Sign Test is a most powerful test.
Derivatives of the inverse trigonometric functions.
Probability of 1st Quadrant for a Standard Bivariate Normal Random Variable.
Wilcoxon Signed Rank Distribution (Part 1).
Wilcoxon Signed Rank Distribution (Part 2).
Wilcoxon Signed Rank Test Statistic define as # of positive Walsh Averages.
Mean and Variance of Wilcoxon Signed Rank Test Statistics.
Interesting Formula for the Sample Variance. U Statistics.
Variance of the sample variance.
Projection method to show normality.
Integrating an inverse cdf of a normal distribution. Normal Scores Statistic.
Covariance of Empirical CDF.
Probability Integral Transformation.
Show that the Kolmogorov-Smirnov One Sample Test is Distribution Free.
Correlation between variate values and corresponding ranks (part 1).
Correlation between variate values and corresponding ranks (part 2).
Correlation between variate values and corresponding ranks (part 3): Illustration Using R..
Probability of 4th Quadrant for a Standard Bivariate Normal Random Variable.
The Univariate Sign Test.
The Multivariate Sign Test.
Probability of 1st Quadrant for a Scaled Bivariate Normal Random Variable.
Using R: The Multivariate Sign Test.
Power and Sample Size in R: Multivariate Sign Test.
Spearman's Rank Correlation.
Kendall's Tau Rank Correlation.
Distribution of the Sample Median.
CI for Population Median using Order Statistics.
Distribution of the Sample Range.
Discrete Order Statistics with Illustration using R.
Integrating over a Rectangle in Polar Coordinates.

Taught by

statisticsmatt

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