We consider multivariate small area estimation under nonignorable, not missing at random(NMAR) nonresponse. We assume a response model that accounts for the different patterns ofthe observed outcomes, (which values ar...We consider multivariate small area estimation under nonignorable, not missing at random(NMAR) nonresponse. We assume a response model that accounts for the different patterns ofthe observed outcomes, (which values are observed and which ones are missing), and estimatethe response probabilities by application of the Missing Information Principle (MIP). By this principle, we first derive the likelihood score equations for the case where the missing outcomes areactually observed, and then integrate out the unobserved outcomes from the score equationswith respect to the distribution holding for the missing data. The latter distribution is definedby the distribution fitted to the observed data for the respondents and the response model. Theintegrated score equations are then solved with respect to the unknown parameters indexingthe response model. Once the response probabilities have been estimated, we impute the missing outcomes from their appropriate distribution, yielding a complete data set with no missingvalues, which is used for predicting the target area means. A parametric bootstrap procedure isdeveloped for assessing the mean squared errors (MSE) of the resulting predictors. We illustratethe approach by a small simulation study.展开更多
文摘We consider multivariate small area estimation under nonignorable, not missing at random(NMAR) nonresponse. We assume a response model that accounts for the different patterns ofthe observed outcomes, (which values are observed and which ones are missing), and estimatethe response probabilities by application of the Missing Information Principle (MIP). By this principle, we first derive the likelihood score equations for the case where the missing outcomes areactually observed, and then integrate out the unobserved outcomes from the score equationswith respect to the distribution holding for the missing data. The latter distribution is definedby the distribution fitted to the observed data for the respondents and the response model. Theintegrated score equations are then solved with respect to the unknown parameters indexingthe response model. Once the response probabilities have been estimated, we impute the missing outcomes from their appropriate distribution, yielding a complete data set with no missingvalues, which is used for predicting the target area means. A parametric bootstrap procedure isdeveloped for assessing the mean squared errors (MSE) of the resulting predictors. We illustratethe approach by a small simulation study.
