Non-parametric Methods

  1. Fundamental Concepts and Tools
    1. Order Statistics
      1. Definition and Basic Properties
        1. Sample Minimum and Maximum
          1. Sample Range
            1. Sample Quantiles
              1. First Quartile
                1. Median
                  1. Third Quartile
                    1. Percentiles
                    2. Distribution of Order Statistics
                      1. Applications in Non-parametric Testing
                      2. Ranking Procedures
                        1. Basic Ranking Methods
                          1. Ascending Ranks
                            1. Descending Ranks
                            2. Handling Tied Observations
                              1. Average Ranks Method
                                1. Mid-ranks Method
                                  1. Random Assignment
                                  2. Signed Ranks
                                    1. Definition and Calculation
                                      1. Applications in Testing
                                    2. Empirical Distribution Function
                                      1. Definition and Construction
                                        1. Properties of the EDF
                                          1. Glivenko-Cantelli Theorem
                                            1. Dvoretzky-Kiefer-Wolfowitz Inequality
                                              1. Applications in Goodness-of-fit Testing
                                              2. Basic Probability Concepts
                                                1. Exact Distributions
                                                  1. Binomial Distribution
                                                    1. Hypergeometric Distribution
                                                    2. Asymptotic Approximations
                                                      1. Normal Approximation
                                                        1. Chi-square Approximation
                                                        2. Continuity Corrections

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                                                      1. Introduction to Non-parametric Statistics

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                                                      3. One-Sample Tests