On a Scheme of Sampling of Two Units With Inclusion With Inclusion

Authors

  • Sarat C. Senapati Ravenshaw College, Cuttack, India
  • L.N. Sahoo Utkal University, Bhubaneswar, India
  • G. Mishra Utkal University, Bhubaneswar, India

DOI:

https://doi.org/10.17713/ajs.v35i4.354

Abstract

This paper introduces an unequal probability sampling without replacement scheme with inclusion probability proportional to size. This new scheme possesses some desirable properties with regard to ?i and ?ij , and provides a non-negative variance estimator of the Horvitz and Thompson estimator, when the values of the auxiliary variable fulfill some restrictions. On comparing the suggested scheme with some of the existing sampling schemes in respect of efficiency and stability of the variance estimator empirically, it has been observed that the performance of the scheme is satisfactory.

References

Brewer, K. R. W. (1963). Ratio estimation in finite populations: Some results deducible from the assumption of an underlying stochastic process. Australian Journal of

Statistics, 5, 93-105.

Brewer, K. R.W., and Hanif, M. (1983). Sampling with Unequal Probabilities. Springer-Verlag.

Chaudhuri, A., and Vos, J. W. E. (1988). Unified Theory and Strategies of Survey Sampling. North Holland.

Cochran, W. G. (1977). Sampling Techniques (3rd ed.). John Wiley and Sons.

Deshpande, M. N., and Prabhu Ajgaonkar, S. G. (1982). An IPPS (inclusion probability proportional to size) sampling scheme. Statistica Neerlandica, 36, 209-212.

Hanurav, T. V. (1967). Optimum utilization of auxiliary information: πs sampling of two units from a stratum. Journal of the Royal Statistical Society, B, 29, 374-391.

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.

Konijn, H. S. (1973). Statistical Theory of Sample Survey Design and Analysis. North Holland.

Mukhopadhyay, P. (1998). Theory and Methods of Survey Sampling. New Delhi: Prentice-Hall of India.

Murthy, M. N. (1957). Ordered and unordered estimators in sampling without replacement. Sankhyˆa, 18, 379-390.

Raj, D. (1956). Some estimators in sampling with varying probabilities without replacement. Journal of the American Statistical Association, 51, 269-284.

Rao, J. N. K., Hartley, H. O., and Cochran, W. G. (1962). A simple procedure of unequal probability sampling without replacement. Journal of the Royal Statistical Society,

B, 24, 482-491.

Sen, A. R. (1953). On the estimator of the variance in sampling with varying probabilities. Journal of the Indian Society of Agricultural Statistics, 5, 119-127.

Singh, D., and Chaudhary, F. S. (1986). Theory and Analysis of Sample Survey Designs. Wiley Eastern Limited.

Singh, P. (1978). The selection of samples of two units with inclusion probability proportional to size. Biometrika, 65, 450-454.

Singh, R., and Singh Mangat, N. (1996). Elements of Survey Sampling. The Netherlands: Kluwer Academic Publishers.

Sukhatme, P. V., and Sukhatme, B. V. (1970). Sampling Theory of Surveys with Applications. Calcutta: Asia Publishing House.

Yates, F. (1953). Sampling Methods for Censuses and Surveys. London: Charles Griffin & Company.

Yates, F., and Grundy, P. M. (1953). Selection without replacement from within strata with probability proportional to size. Journal of the Royal Statistical Society, B, 15, 235-261.

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Published

2016-04-03

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Articles

How to Cite

On a Scheme of Sampling of Two Units With Inclusion With Inclusion. (2016). Austrian Journal of Statistics, 35(4), 445–454. https://doi.org/10.17713/ajs.v35i4.354