RESPONSE MODEL SELECTION IN SMALL AREA ESTIMATION IN CASE OF NOT MISSING AT RANDOM NONRESPONSE AND ONLY TOTALS AVAILABLE FOR AUXILIARY VARIABLES

Music City Center 

Sverchkov and Pfeffermann (S-P, 2023) suggested Information Criteria, similar to AIC and BIC for response model selection for Small Area Estimation under informative probability sampling of areas and within the sampled areas and not missing at random (NMAR) nonresponse. The approach considered by S-P requires knowledge of auxiliary data for complete sample before response occurs. In this paper we generalize this approach to the case where auxiliaries are not known for the non-respondents, but their totals are known.
REFERENCES
Sverchkov and Pfeffermann (2023), Response Model Selection in Small Area Estimation Under not Missing at Random Nonresponse. Calcutta Statistical Association Bulletin, pp. 1 -11

information criteria

likelihood ratio tests

missing information principle

non-probability sampling