5.2 Create missing values of Y2 for the data in Problem 5.1 by generating a latent variable U with values ui = 2∗( yi1 −1) + zi3, where zi3 is a standard normal deviate, and setting yi2 as missing when ui <0. This mechanismismissing at random (MAR) because U depends on Y1 but not Y2.

With U having mean 0, about half of the values of Y2 should be missing.

Impute the missing values of Y2 using conditional means from the linear regression of Y2 on Y1, estimated from the complete units. Compute standard errors of estimates of the mean of Y2 and coefficient of variation of Y2 from the filled-in data, using the bootstrap and jackknife, applied both after imputation and before imputation; that is, for each replication of incomplete data, impute all missing values and estimate parameters.

Which of these methods yield 90% intervals that actually cover the true parameter about 90% of the time? Which are theoretically valid, in the sense of yielding correct confidence interval coverage in large samples?