Event
Saraswata Chaudhuri, Department of Economics, McGill University
Wednesday, March 21, 2018 15:30to16:30
Room D-4, Université de Sherbrooke, 2500 Boul. de l'Université, QC, J1K 2R1, CA
Efficient estimation in sub and full populations with monotonically missing at random data.
We consider estimation of a parameter defined by moment restrictions on a target population charac- terized by the missingness pattern of monotonically missing at random data. Attrition or dropout in a, say, R-period study/survey typically generates such data. In this case, a generic target is the underlying population of the sample units dropping out in contiguous periods a, . . . , b where a <= b in {1, . . . , R}. The semiparametric efficiency bound and the efficient influence function are obtained for the parameter of interest from the generic target nesting the well-known special cases with (a = 1, b = R) or (R = 2, a = b = 1). Our results, however, differ fundamentally from the existing literature in that the consideration of a generic target beyond those special cases provides new insights on the usability and contribution of the sam- ple units toward efficient estimation. Efficient estimation turns out to be standard MINPIN estimation with asymptotic properties directly following from the well-known existing results. Further desirable properties follow since the concerned MINPIN estimating functions are also doubly robust to parametric misspecifica- tion of the nonparametric nuisance components. A Monte Carlo study demonstrates all these nice properties of the efficient estimator and the t-test based on it. A simple empirical illustration using the Project STAR data demonstrates substantive improvement in precision over the standard but inefficient estimators.We consider estimation of a parameter defined by moment restrictions on a target population charac- terized by the missingness pattern of monotonically missing at random data. Attrition or dropout in a, say, R-period study/survey typically generates such data. In this case, a generic target is the underlying population of the sample units dropping out in contiguous periods a, . . . , b where a <= b in {1, . . . , R}. The semiparametric efficiency bound and the efficient influence function are obtained for the parameter of interest from the generic target nesting the well-known special cases with (a = 1, b = R) or (R = 2, a = b = 1). Our results, however, differ fundamentally from the existing literature in that the consideration of a generic target beyond those special cases provides new insights on the usability and contribution of the sam- ple units toward efficient estimation. Efficient estimation turns out to be standard MINPIN estimation with asymptotic properties directly following from the well-known existing results. Further desirable properties follow since the concerned MINPIN estimating functions are also doubly robust to parametric misspecifica- tion of the nonparametric nuisance components. A Monte Carlo study demonstrates all these nice properties of the efficient estimator and the t-test based on it. A simple empirical illustration using the Project STAR data demonstrates substantive improvement in precision over the standard but inefficient estimators.