Root-n estimability of some missing data models

It is known that in many missing data models, for example, survival data models, some parameters are root-n estimable while the others are not. When they are, their limiting distributions are often Gaussian and easy to use. When they are not, their limiting distributions, if exists, are often non-Gaussian and difficult to evaluate. Thus it is important to have some preliminary assessments of the root-n estimability in these models. In this article, we study this problem for four missing data models: two-point interval censoring, double censoring, interval truncation, and a case-control genetic association model. For the first three models, we identify some parameters which are not root-n estimable. For some root-n estimable parameters, we derive the corresponding information bounds when they exist. Also, as the Cox regression model is commonly used for such data, we give asymptotic efficient information for these regression parameters. For the case-control genetic association model, we compute the asymptotic efficient information and relative efficiency, in relation to that of the full data, when only the case-control status data are available, as is often the case in practice.