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On ordinary least-squares methods for sample surveys

Publication ,  Journal Article
Wang, SG; Chow, SC; Tse, SK
Published in: Statistics and Probability Letters
June 22, 1994

The performance of the ordinary least-squares (LS) method for two-stage sampling in regression analysis is studied. It is shown that the best linear unbiased estimator (BLUE) can be approximated by a polynomial in intracluster correlation. In particular, the least-squares estimator (LSE) is a zero-order approximation to the BLUE. To provide some insights into the approximation of the BLUE by the LSE, an upper bound for the difference between LSE and the first-order approximation to the BLUE is derived. Furthermore, bounds for the difference between the covariance matrices of the LSE and the BLUE are derived. Similar idea is applied to compare the LS and the BLU predictors of population total under a superpopulation model. For example, when the design matrix is ill-conditioned and/or the condition number of the covariance matrix of the error vector is large, the LSE has a poor performance compared to the BLUE. © 1994.

Duke Scholars

Published In

Statistics and Probability Letters

DOI

ISSN

0167-7152

Publication Date

June 22, 1994

Volume

20

Issue

3

Start / End Page

173 / 182

Related Subject Headings

  • Statistics & Probability
  • 1403 Econometrics
  • 0104 Statistics
  • 0102 Applied Mathematics
 

Citation

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Wang, S. G., Chow, S. C., & Tse, S. K. (1994). On ordinary least-squares methods for sample surveys. Statistics and Probability Letters, 20(3), 173–182. https://doi.org/10.1016/0167-7152(94)90039-6
Wang, S. G., S. C. Chow, and S. K. Tse. “On ordinary least-squares methods for sample surveys.” Statistics and Probability Letters 20, no. 3 (June 22, 1994): 173–82. https://doi.org/10.1016/0167-7152(94)90039-6.
Wang SG, Chow SC, Tse SK. On ordinary least-squares methods for sample surveys. Statistics and Probability Letters. 1994 Jun 22;20(3):173–82.
Wang, S. G., et al. “On ordinary least-squares methods for sample surveys.” Statistics and Probability Letters, vol. 20, no. 3, June 1994, pp. 173–82. Scopus, doi:10.1016/0167-7152(94)90039-6.
Wang SG, Chow SC, Tse SK. On ordinary least-squares methods for sample surveys. Statistics and Probability Letters. 1994 Jun 22;20(3):173–182.
Journal cover image

Published In

Statistics and Probability Letters

DOI

ISSN

0167-7152

Publication Date

June 22, 1994

Volume

20

Issue

3

Start / End Page

173 / 182

Related Subject Headings

  • Statistics & Probability
  • 1403 Econometrics
  • 0104 Statistics
  • 0102 Applied Mathematics