A good way to begin this discussion is by quoting from a paper delivered to the ASA some 15 years ago. Talking then of the 1960 census, Walter Perkins and Charles Jones began: “Perhaps it is true that ‘a rose is a rose is a rose’ this is a little outside our field. We do, however, disagree with anyone who makes the same claim for a match.” They then add: “There is a rather mysterious category – ‘the impute;’ the census interviewer has been told that a given address is occupied, but has been unable to find anyone home on repeated visits. The computer has imputed at this address a young couple plus a five year old daughter. ON a revisit, however, we find the occupant at the time of the census was an elderly man. Was he counted – or wasn’t he? It would seem clear that he wasn’t; yet, from another point of view, it appears that he has been counted – not wisely, but too well!!”. The problem of the impute epitomizes a general problem in dual-system estimation: the problem of insufficient or erroneous information. Nonresponse is, of course, a standard problem in survey samples. Indeed, imputations were created as a way to deal with this problem. Further, every survey will contain erroneous responses.
-Hogan, Howard, and Cowan, Charles D.