The Horvitz-Thompson theorem as a unifying perspective for probability sampling: With examples from natural resource sampling

American Statistician

Volumn 49, Issue 3, 1995, Pages 261-268

  Overton, W Scott ^a   Stehman, Stephen V ^b  

^a OREGON STATE UNIVERSITY   (United States)

^b STATE UNIVERSITY OF NEW YORK   (United States)

Author keywords

Bitterlich sampling; Environmental sampling; Inclusion probability; Systematic sampling; Variable probability sampling

Indexed keywords

EID: 21844508117     PISSN: 00031305     EISSN: 15372731     Source Type: Journal    
DOI: 10.1080/00031305.1995.10476160     Document Type: Article

References (27)

1. Avery, T. E., and Burkhart, H. E. (1994), Forest Measurements (4th ed.), New York: McGraw-Hill.
2. Cassel, C. M., Särndal, C. E., and Wretman, J. (1977), Foundations of Inference in Survey Sampling, New York: John Wiley.
3. Cochran, W. G. (1977), Sampling Techniques (3rd ed.), New York: John Wiley.
4. Cox, D. R. (1969), “Some Sampling Problems in Technology,” in New Developments in Survey Sampling, eds. N. L. Johnson and H. Smith, Jr., New York: Wiley Interscience, pp. 506-527.
5. De Vries, P. G. (1986), Sampling Theory for Forest Inventory, New York: Springer-Verlag.
6. Fisher, R. A. (1956), Statistical Methods and Scientific Inference (3rd ed.), New York: Hafner Press.
7. Gilbert, R. O. (1987), Statistical Methods for Environmental Pollution Monitoring, New York: Van Nostrand Reinhold.
8. Hansen, M. H., Hurwitz, W. N., and Madow, W. G. (1953), Sample Survey Methods and Theory, Volume I: Methods and Applications, New York: John Wiley.
9. Hayne, D. W. (1949), “An Examination of the Strip Census Method for Estimating Animal Populations,” Journal of Wildlife Management, 13, 145-157.
10. Horvitz, D. G., and Thompson, D. J. (1952), “A Generalization of Sampling without Replacement from a Finite Universe,” Journal of the American Statistical Association, 47, 663-685.
11. Kaufmann, P. R., Herlihy, A. T., Elwood, J. W., Mitch, M. E., Overton, W. S., Sale, M. J., Messer, J. J., Cougan, K. A., Peck, D. V., Reckhow, K. H., Kinney, A. J., Christie, S- J-, Brown, D. D., Hagley, C. A., and Jager, H. I. (1988), “Chemical Characteristics of Streams in the Mid-Atlantic and Southeastern United States, Volume 1: Population Descriptions and Physico-Chemical Relationships,” EPA/600/3-88/021a, Washington, DC: U.S. Environmental Protection Agency.
12. Kish, L. (1965), Survey Sampling, New York: John Wiley.
13. Kish, L. (1987), Statistical Design for Research, New York: John Wiley.
14. Murthy, M. N. (1967), Sampling Theory and Methods, Calcutta: Statistical Publishing Society.
15. Otis, D. L., McDonald, L. L., and Evans, M. A. (1993), “Parameter Estimation in Encounter Sampling Surveys,” Journal of Wildlife Management, 57, 543-548.
16. Overton, W. S. (1969), “Estimating the Numbers of Animals in Wildlife Populations,” in Wildlife Management Techniques, ed. R. H. Giles, Jr., Washington, DC: The Wildlife Society, pp. 403-455.
17. Overton, W. S., and Stehman, S. V. (1992), “The Horvitz-Thompson Theorem as a Unifying Perspective for Sampling,” in Proceedings of the Section on Statistics Education of the American Statistical Association, Alexandria, VA: American Statistical Association, pp. 380-385.
18. Raj, D. (1968), Sampling Theory, New York: McGraw-Hill.
19. Särndal, C. E. (1980), “On 7r-Inverse Weighting Versus Best Linear Unbiased Weighting in Probability Sampling,” Biometrika, 67, 639-650.
20. Särndal, C. E., Swensson, B., and Wretman, J. (1992), Model Assisted Survey Sampling, New York: Springer-Verlag.
21. Schreuder, H. T., Tyre, G. L” and James, G. A. (1975), “Instant- and Interval Count Sampling: Two New Techniques for Estimating Recreation Use,” Forest Science, 21, 40-44.
22. Schreuder, H. T., Gregoire, T. G., and Wood, G. (1993), Sampling Methods for Multiresource Forest Inventory, New York: John Wiley.
23. Smith, W., and Pames, M. (1994), “Mean Streets: The Median of a Size- Biased Sample and Population Mean,” The American Statistician, 48, 106-110.
24. Stuart, A. (1962), The Basic Ideas of Scientific Sampling (1984 ed.), London: Charles Griffin and Company.
25. Stuart, A. (1964), “Some Remarks on Sampling with Unequal Probabilities,” Bulletin of the International Statistical Institute, 40, 773-779.
26. Webster, R., and Oliver, M. A. (1990), Statistical Methods in Soil and Land Resource Survey, New York: Oxford University Press.
27. Yates, F., and Grundy, P. M. (1953), “Selection Without Replacement from Within Strata with Probability Proportional to Size,” Journal of the Royal Statistical Society, Ser. B, 15, 235-261.