Divide the sample into m independent groups. In most instances (unless the sample size is very large), we take m = n, in which case each observation constitutes a ‘‘group.’’ If the data originate from...

Divide the sample into m independent groups. In most instances (unless the sample size is very large), we take m = n, in which case each observation constitutes a ‘‘group.’’ If the data originate from a cluster sample, then the observations in a cluster should be kept together.

(a) 'Show that when the jackknife procedure is applied to the mean with m = n, the pseudo-values are just the original observations, bθ'
_i
= Y_i; the jackknifed estimate bθ' is, therefore, the sample mean Y; and the jackknifed confidence interval is the same as the usual t confidence interval.

(b) Demonstrate the results in part (a) numerically for the contrived ‘‘data’’ in Table 21.3. (These results are peculiar to linear statistics like the mean.)

(c) Find jackknifed confidence intervals for the Huber M estimator of Duncan’s regression of occupational prestige on income and education. Compare these intervals with the bootstrap and normal-theory intervals given in Table 21.5.