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Improved variance estimation for inequality-constrained domain mean estimators using survey data. (English) Zbl 1477.62084

Summary: In survey domain estimation, a priori information can often be imposed in the form of linear inequality constraints on the domain estimators. J. Wu et al. [Can. J. Stat. 44, No. 4, 431–444 (2016; Zbl 1357.62056)] formulated the isotonic domain mean estimator, for the simple order restriction, and methods for more general constraints were proposed in C. Oliva-Avilés et al. [“Estimation and inference of domain means subject to qualitative constraints”, Surv. Methodol. 46, No. 2, 145–180 (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. Here, 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.

MSC:

62G05 Nonparametric estimation
62G08 Nonparametric regression and quantile regression
62G15 Nonparametric tolerance and confidence regions
62H12 Estimation in multivariate analysis
62D05 Sampling theory, sample surveys
62D20 Causal inference from observational studies
60E15 Inequalities; stochastic orderings

Citations:

Zbl 1357.62056

Software:

coneproj
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References:

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