Orthogonal Series Density Estimation for Complex Surveys

TL;DR

This paper introduces an orthogonal series density estimator tailored for complex survey data, ensuring unbiasedness and consistency despite dependencies, with demonstrated efficiency through simulations and real data application.

Contribution

It develops a novel orthogonal series density estimator for complex surveys, addressing dependence issues and providing data-driven variants with proven theoretical properties.

Findings

Estimator is design-unbiased and asymptotically consistent.

Proposed estimators are efficient in simulation studies.

Real survey data example illustrates practical applicability.

Abstract

We propose an orthogonal series density estimator for complex surveys, where samples are neither independent nor identically distributed. The proposed estimator is proved to be design-unbiased and asymptotically design-consistent. The asymptotic normality is proved under both design and combined spaces. Two data driven estimators are proposed based on the proposed oracle estimator. We show the efficiency of the proposed estimators in simulation studies. A real survey data example is provided for an illustration.