Skip to main content
SpringerLink
Log in

On the axioms of sample formation and their bearing on the construction of linear estimators in sampling theory for finite universes

  • Veröffentlichungen
  • Published:
Metrika Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  • Bailey, N. T. J. (1951). On estimating the size of mobile populattons from recapture data. Biometrika,38, 292–306.

    Google Scholar 

  • Basu, D. (1954): On the opttmum character of some estimators used in multistage sampling problems. Sankhyā,13, 363–368.

    MATH  Google Scholar 

  • —— (1958): On sampling with and without replacement. Sankhya,20, 287–294.

    MATH  MathSciNet  Google Scholar 

  • Blackwell, D. (1947): Conditional expectation and unbiased sequential estimation. Ann. Math. Statist.,18, 105–110.

    MathSciNet  MATH  Google Scholar 

  • Chapman, D. G. (1952): Inverse, multiple and sequential sample censuses. Biometrics,8, 286–306.

    Article  MathSciNet  Google Scholar 

  • Cochrane, W. G. (1946): Relative accuracy of systematic and stratified random samples for a certain class of populations. Ann. Math. Statist.,17, 164–177.

    Google Scholar 

  • Dalenius, T. (1962): Recent advances in sample survey theory and methods. Ann. Math. Statist.,33, 325–349.

    MathSciNet  MATH  Google Scholar 

  • David, F. N., andBarton, D. E. (1962):Combinatorial Chance. Charles Griffin and Co. Ltd., London.

    Google Scholar 

  • Das, A. C. (1951): On two-phase sampling and sampling with varying probabilities. Bull. Inst. Internat. Statist.,33, 105–112.

    Google Scholar 

  • Des Raj (1954): Ratio estimation in sampling with equal and unequal probabilities. J. Indian. Soc. Agric. Statist.,5, 127–138.

    MathSciNet  Google Scholar 

  • —— (1956): Some estimators in sampling with varying probabilities without replacement. J. Amer. Statist. Assoc.,51, 269–284.

    Article  MATH  MathSciNet  Google Scholar 

  • —— (1956a): A note on the determination of optimum probabilities in sampling without replacement. Sankhya,17, 197–200.

    MATH  MathSciNet  Google Scholar 

  • Des Raj andKhamis, S. H. (1958): Some remarks on sampling with replacement. Ann. Math. Statist.,29, 550–557.

    MathSciNet  MATH  Google Scholar 

  • Durbin, J. (1953): Some results in sampling theory when the units are selected with unequal probabilities. J. Roy. Statist. Soc., B15, 262–269.

    MATH  Google Scholar 

  • Feller, W. (1950):An Introduction to Probability Theory and its Applications I. John Wiley and Sons Inc., New York.

    MATH  Google Scholar 

  • Fisher, R. A. (1922): On the mathematical foundations of theoretical statistics. Philos. Trans. Roy. Soc. London Ser. A222, 309–368.

    Google Scholar 

  • Fisher, R. A., andYates, F. (1938, 1953): Statistical Tables for Biological, Agricultural and Medical Research. (1st ed.-) Oliver and Boyd, Edinburgh.

    MATH  Google Scholar 

  • Godambe, V. P. (1955): A unified theory of sampling from finite populations. J. Roy. Statist. Soc., B17, 269–278.

    MATH  MathSciNet  Google Scholar 

  • Hajek, J. (1949): Representativní vgber skupin methodou dvou fází. Statisticky Obzor.,29′ 384–394.

    Google Scholar 

  • Hansen, M. H., andHurwitz, W. N. (1943): On the theory of sampling from finite populations. Ann. Math. Statist.,14, 333–362.

    MathSciNet  MATH  Google Scholar 

  • —— (1949): On the determination of optimum probabilities in sampling. Ann. Math. Statist.,20, 426–432.

    MATH  Google Scholar 

  • Hartley, H. O., andRao, J. N. K. (1962): Sampling with unequal probabilities and without replacement. Ann. Math. Statist.,33, 350–374.

    MathSciNet  MATH  Google Scholar 

  • Horvitz, D. G., andThompson, D. J. (1951): A generalization of sampling without replacement from a finite universe (Abstract). Ann. Math. Statist.,22, 315.

    Google Scholar 

  • —— (1952): Ibid. J. Amer. Statist. Assoc.,47, 663–685.

    Article  MATH  MathSciNet  Google Scholar 

  • Koop, J. C. (1957): Contributions to the general theory of sampling finite populations without replacement and with unequal probabilities. Ph. D. Thesis. N. Carolina State College Library, Raleigh. (Inst. of Statistics, Mimeo Series No. 296, 1961).

    Google Scholar 

  • —— (1961): On the higher moments of linear estimates based on multistage samples from a finite population (Abstract). Ann. Math. Stat.,32, 628.

    Google Scholar 

  • —— (1962): Some remarks on negative estimates of variance in unequal probability sampling (Abstract). Ann. Math. Statist.,33, 1495.

    Google Scholar 

  • Koop, J. C. (unpublished): On the theory of the Friedman-Wilcox method of sampling extended to units each composed of aggregates of smaller units.

  • Lahiri, D. B. (1951): A method of sample selection providing unbiased ratio estimates. Bull. Inst. Internat. Statist.,33, 133–140.

    Google Scholar 

  • Madow, W. G. (1949): On the theory of systematic sampling, II. Ann. Math. Statist.,20, 333–354.

    MathSciNet  MATH  Google Scholar 

  • Midzuno, H. (1950): An outline of the theory of sampling systems. Ann. Inst. Statist. Math. Tokyo,1, 149–156.

    MATH  MathSciNet  Google Scholar 

  • —— (1952): On the sampling system with probability proportionate to sum of sizes. Ibid,3, 99–107.

    MATH  MathSciNet  Google Scholar 

  • Mickey, M. R. (1959): Some finite population unbiased ratio and regression estimators. J. Amer. Statist. Assoc.,54, 594–612.

    Article  MATH  MathSciNet  Google Scholar 

  • Murthy, M. N. (1957): Ordered and unordered estimators in sampling without replacement. Sankhyā,18, 379–390.

    MATH  MathSciNet  Google Scholar 

  • Narain, R. D. (1951): On sampling without replacement with varying probabilities. J. Indian Soc. Agric. Statist.,3, 169–174.

    MathSciNet  Google Scholar 

  • Neyman, J. (1938): Contribution to the theory of sampling human populations. J. Amer. Statist. Assoc.,33, 101–116.

    Article  MATH  Google Scholar 

  • Pathak, P. K. (1961): Use of “order-statistic” in sampling without replacement. Sankhyā, A23, 409–414.

    MATH  MathSciNet  Google Scholar 

  • Pearson, K. (1916): Mathematical contributions to the theory of evolution XIX; second supplement to a memoir in skew variation. Philos. Trans. Roy. Soc. London Ser. A216, 429–457.

    Google Scholar 

  • Rao, C. R. (1945): Information and the accuracy attainable in the estimation of statistical parameters. Bull. Calcutta Math. Soc.,37, 81–91.

    MATH  MathSciNet  Google Scholar 

  • Rao, J. N. K., Hartley, H. O., andCochrance, W. G. (1962): On a simple procedure of unequal probability sampling without replacement. J. Roy. Statist. Soc., B24, 482–491.

    MATH  Google Scholar 

  • Sampford, M. R. (1962): Methods of cluster sampling with and without replacement for clusters of unequal sizes. Biometrika,49, 27–40.

    MATH  MathSciNet  Google Scholar 

  • Sen, A. R. (1952): Further developments of the theory and application of primary sampling units with special reference to the North Carolina agricultural population. Ph. D. Thesis, N. Carolina State College Library, Raleigh.

    Google Scholar 

  • —— (1953): On the estimate of the variance in sampling with varying probabilities. J. Indian Soc. Agric. Statist.,5, 119–127.

    MathSciNet  Google Scholar 

  • Sen, A. R., Anderson, R. L., andFinkner, A. L. (1954): A comparison of stratified two-stage sampling systems. J. Amer. Statist. Soc.,49, 539–558.

    Google Scholar 

  • Sukhatme, P. V. (1954):Sampling Theory of Surveys with Applications. The Indian Society of Agricultural Statistics, New Delhi, India, and The Iowa State College Press, Ames, Iowa.

    MATH  Google Scholar 

  • Sukhatme, P. V., andNarain, R. D. (1952): Sampling with replacement. J. Indian. Soc. Agric. Statist.,4, 42–49.

    MathSciNet  Google Scholar 

  • Taeuber, R. C., (1961): Sampling with replacement: an axiomatic approach. Ph.D. Thesis, N. Carolina State College Library, Raleigh.

    Google Scholar 

  • Thompson, D. J. (1952): A theory of sampling finite universes with arbitrary probabilities. Ph. D. Thesis, Iowa State University, Ames.

    Google Scholar 

  • Wilkins, J. E. (1944): A note on skewness and kurtosis. Ann. Math. Statist.,15, 333–335.

    MathSciNet  MATH  Google Scholar 

  • Yamamoto, S. (1955): On the theory of sampling with probabilities proportionate to given values. Ann. Inst. Statist. Math. Tokyo,7, 25–38.

    Article  MATH  MathSciNet  Google Scholar 

  • Yates, F. (1948): Systematic sampling. Philos. Trans. Roy. Soc. London Ser. A,241, 345–377.

    MathSciNet  MATH  Google Scholar 

  • Yates, F., andGrundy, P. M. (1953): Selection without replacement from within strata with probability proportional to size. J. Roy. Statist. Soc., B15, 253–261.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. N. Carolina State College, Raleigh, North Carolina

    J. C. Koop (Associate Professor of Experimental Statistics)

Authors
  1. J. C. Koop
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Koop, J.C. On the axioms of sample formation and their bearing on the construction of linear estimators in sampling theory for finite universes. Metrika 7, 81–114 (1963). https://doi.org/10.1007/BF02613965

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02613965

Keywords

Search

Navigation