212 Introduction to Robust Estimation and Hypothesis Testing 5.10 Exercises 1. Compare the two groups of data in Table 5.1 using the weighted Kolmogorov­Smirnov test. Plot the shift function and its 0.95 confidence band. Compare the results with the unweighted test. 2. Compare the two groups of data in Table 5.3 using the weighted Kolmogorov­Smirnov test. Plot the shift function and its 0.95 confidence band. Compare the results with the unweighted test. 3. Summarize the relative merits of using the weighted versus unweighted Kolmogorov­Smirnov test. Also discuss the merits of the Kolmogorov­Smirnov test relative to comparing measures of location. 4. Consider two independent groups having identical distributions. Suppose four observations are randomly sampled from the first and three from the second. Determine P(D = 1) and P(D = 0.75), where D is given by Eq. (5.4). Verify your results with the R function kssig. 5. Compare the deciles only, using the Harrell­Davis estimator, using the data in Table 5.1. 6. Verify that if X and Y are independent, the third moment about the mean of X - Y is µ x[3] - µ y[3] . 7. Apply the Yuen­Welch method to the data in Table 5.1 where the amount of trimming is