Orthogonal series density estimation for complex surveys

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.

KEYWORDS:

• Nonparametric
• asymptotic
• survey sampling
• orthogonal basis
• Horvitz–Thompson estimator
• mean integrated squared error

Acknowledgments

We thank an associate editor and a referee for their constructive comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Ye Liang  http://orcid.org/0000-0002-6513-8962

Additional information

Funding

This research is partially supported by National Science Foundation [grant number OIA-1301789].