A Variance Estimator for Systematic Sampling from a Deliberately Ordered Population

• Published in: Communications in statistics. Theory and methods Vol. 34; no. 7; pp. 1533 - 1541
• Main Author: Berger, Yvesg G.
• Format: Journal Article
• Language: English
• Published: Philadelphia, PA Taylor & Francis Group 01.07.2005; Taylor & Francis
• Subjects: Applied sciences; Distribution theory; Exact sciences and technology; Inclusion probabilities; Information, signal and communications theory; Mathematics; Primary 62D05; Probability and statistics; Sampling theory, sample surveys; Sampling, quantization; Sciences and techniques of general use; Secondary 94A20; Signal and communications theory; Statistics; Telecommunications and information theory; Unequal probability sampling; Weighted least squares; π-estimator; Monte Carlo method; Weighted least squares. Primary 62D05; Variance estimation; Inclusion probabilities; Unequal probability sampling; π-estimator; Probability distribution; Sampling design; Statistical simulation; Statistical method; Secondary 94A20; Systematic sampling; Least squares method; Biased estimation
• ISSN: 0361-0926; 1532-415X
• DOI: 10.1081/STA-200063383

The systematic sampling (SYS) design (Madow and Madow, 1944 ) is widely used by statistical offices due to its simplicity and efficiency (e.g., Iachan, 1982 ). But it suffers from a serious defect, namely, that it is impossible to unbiasedly estimate the sampling variance (Iachan, 1982 ) and usual variance estimators (Yates and Grundy, 1953 ) are inadequate and can overestimate the variance significantly (Särndal et al., 1992 ). We propose a novel variance estimator which is less biased and that can be implemented with any given population order. We will justify this estimator theoretically and with a Monte Carlo simulation study.