4.12 Another method for generating imputations is the sequential hot deck, where responding and nonresponding units are treated in a sequence, and a missing value of Y is replaced by the nearest responding value preceding it in the sequence. For example, if n = 6, r = 3, y1, y4, and y5 are observed, and y2, y3, and y6 are missing, then y2 and y3 are replaced by y1, and y6 is replaced by y5. If y1 is missing, then some starting value is used (for example, a value chosen from records in a prior survey). This method formed the basis for early imputation schemes for the US Census Bureau’s Current Population Survey.

84 4 Single Imputation Methods Suppose a simple random sample and a Bernoulli missingness mechanism.

Show that the sequential hot deck estimate of Y, say yHD3, is unbiased for Y with sampling variance (for large r and n and ignoring finite population corrections) given by Var( yHD3) = (1 + (n − r)∕n)S2∕r.

Hence, the proportionate increase in sampling variance over yR is

(n−r)/n, the fraction of missing data (see Bailar et al. 1978, for details).