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Regression estimator in ranked set sampling

P L Yu1, K Lam

  • 1Department of Statistics, University of Hong Kong.

Biometrics
|October 23, 1997
PubMed
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Ranked set sampling (RSS) with regression on a concomitant variable improves population mean estimation. This method is more efficient than simple random sampling (SRS) and standard RSS, especially with correlated variables.

Area of Science:

  • Statistics
  • Survey Methodology
  • Environmental Science

Background:

  • Ranked set sampling (RSS) enhances precision for population mean estimation using auxiliary ranking information.
  • Auxiliary variable ranking in RSS may be imperfect, impacting estimator accuracy.

Purpose of the Study:

  • Propose novel regression-type RSS estimators for population mean of Y using a concomitant variable X.
  • Investigate estimator performance when the mean of X is known and unknown (using double sampling).

Main Methods:

  • Develop regression-type RSS estimators incorporating a concomitant variable X for ranking and estimation.
  • Employ double sampling to estimate the population mean of X when unknown.
  • Analyze estimator efficiency under bivariate normal distribution and non-normal scenarios.

Related Experiment Videos

Main Results:

  • The proposed RSS regression estimator outperforms standard RSS and simple random sampling (SRS) naive estimators when X and Y are bivariate normal (correlation > 0.4).
  • The estimator is consistently superior to SRS regression estimators across all correlation levels.
  • The method shows robustness to slight departures from normality in X's distribution.

Conclusions:

  • Regression-type RSS offers a more precise and efficient method for estimating population means, particularly in environmental studies.
  • The proposed estimators provide significant gains in efficiency over traditional methods under specific distributional assumptions.
  • Robustness to non-normality and a remedial measure for skewed distributions enhance practical applicability.