Repeat Exercise 4 ten times, using different random digits each time. In other words, construct ten independent samples each of which contains 15 observations and each of which satisfies the conditions of Exercise 4.
(a) For each sample, which of the estimators listed in Exercise 4 is closest to O?
(b) For each of the estimators listed in Exercise 4, determine the square of the distance between the estimator and 0 in each of the ten samples, and determine the average of these ten squared distances. For which of the estimators is this average squared distance from 0 smallest?
Exercise 4
Use the table of random digits given at the end of this book to obtain a sample of 15 independent observations in which 13 of the 15 are drawn from the uniform distribution on the interval (-1.1) and the other two are drawn from the uniform distribution on the interval (- 10, 10). For the 15 values that are obtained, calculate the values of (a) the sample mean; (b) the trimmed means for k = 1, 2, 3, and 4; and (c) the sample median. Which of these estimators is closest to O?