Some topics on survey estimators under shape constraints

2021 Summer.Includes bibliographical references.We consider three topics in this dissertation: 1) Nonresponse weighting adjustment using estimated response probability; 2) Improved variance estimation for inequality constrained domain mean estimators in surveys; and 3) One-sided testing of population domain means in surveys. Weighting by the inverse of the estimated response probabilities is a common type of adjustment for nonresponse in surveys. In the first topic, we propose a new survey estimator under nonresponse where we set the response model in linear form and the parameters are estimated by fitting a constrained least square regression model, with the constraint being a calibration equation. We examine asymptotic properties of Horvitz-Thompson and Hájek versions of the estimators. Variance estimation for the proposed estimators is also discussed. In a limited simulation study, the performances of the estimators are compared with those of the corresponding uncalibrated estimators in terms of unbiasedness, MSE and coverage rate. In survey domain estimation, a priori information can often be imposed in the form of linear inequality constraints on the domain estimators. Wu et al. (2016) formulated the isotonic domain mean estimator, for the simple order restriction, and methods for more general constraints were proposed in Oliva-Avilés et al. (2020). When the assumptions are valid, imposing restrictions on the estimators will ensure that the a priori information is respected, and in addition allows information to be pooled across domains, resulting in estimators with smaller variance. In the second topic, we propose a method to further improve the estimation of the covariance matrix for these constrained domain estimators, using a mixture of possible covariance matrices obtained from the inequality constraints. We prove consistency of the improved variance estimator, and simulations demonstrate that the new estimator results in improved coverage probabilities for domain mean confidence intervals, while retaining the smaller confidence interval lengths. Recent work in survey domain estimation allows for estimation of population domain means under a priori assumptions expressed in terms of linear inequality constraints. Imposing the constraints has been shown to provide estimators with smaller variance and tighter confidence intervals. In the third topic, we consider a formal test of the null hypothesis that all the constraints are binding, versus the alternative that at least one constraint is non-binding. The test of constant versus increasing domain means is a special case. The power of the test is substantially better than the test with an unconstrained alternative. The new test is used with data from the National Survey of College Graduates, to show that salaries are positively related to the subject's father's educational level, across fields of study and over several years of cohorts