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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

Description:

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.

Nonparametric Theory

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#Mathematics #Statistics & Probability #Hypothesis Testing

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