Orthogonal series density estimation for complex surveys. Issue 2 (3rd April 2019)

• Record Type: Journal Article
• Authors: Ye, Shangyuan; Liang, Ye; Ahmad, Ibrahim A.
• Is Part Of: Journal of nonparametric statistics. Volume 31:Issue 2(2019)
• Page Start: 469
• Page End: 481
• Publication Date: 2019-04-03
• Subjects: Nonparametric -- asymptotic -- survey sampling -- orthogonal basis -- Horvitz–Thompson estimator -- mean integrated squared error; Nonparametric statistics -- Periodicals; 519.5
• DOI: 10.1080/10485252.2019.1585539
• Languages: English
• ISSNs: 1048-5252

Abstract

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.