A note on convergence of calibration weights to inverse probability weights

Recently, nonresponse rates in sample surveys have been increasing. Nonresponse bias is a serious concern in the analysis of sample surveys. The calibration and propensity score methods are used to adjust nonresponse bias. The propensity score method uses the weights of the inverse probability of response. The inverse probability of response is estimated by the auxiliary variables observed in respondents and nonrespondents. The calibration method can use additional auxiliary variables observed only in respondents if the population distributions of the variables are known. The calibration method is widely used; however, the theoretical property in the nonresponse situation has not been investigated. This study provides a condition that the calibration weights asymptotically go to the inverse probability of response and clarifies the relationship between the calibration and propensity score methods.