Abstract
The paper surveys admissibility and uniform admissibility results in finite population sampling starting with the pioneering work of Professor Joshi, Professor Godambe and others. The recently introduced “stepwise Bayes” technique of Meeden and Ghosh has been explored in the proof of admissibility of well-known estimators as well as in the construction of new admissible estimators of the finite population mean and the finite population variance.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Basu, D. (1971), “An essay on the logical foundations of survey sampling, part one.” In Foundations of Statistical Inference, ed. V. P. Godambe and D. A. Sprott, pp. 203 – 242. Toronto: Holt, Rinehart and Winston.
Binder, D. A. (1982), “Non-parametric Bayesian models for samples from finite populations.” Journal of the Royal Statistical Society, Series B 44, 388–393.
Biyani, S. H. (1980), “On inadmissibility of the Yates-Grundy variance estimator in unequal probability sampling”. Journal of the American Statistical Association 75, 709–712.
Brewer, K. R. W. (1979), “A class of robust sampling designs for large-scale surveys.” Journal of the American Statistical Association 74, 911–915.
Cassel, C. M., C. E. Sarndal, and J. H. Wretman (1977), Foundations of Inference in Survey Sampling. New York: Wiley and Sons.
Chaudhuri, A. (1978), “On estimating the variance of a finite population.” Metrika 25, 65–76.
Cohen, M. P., and L. Kuo (1985), “The admissibility of the empirical distribution function.” Annals of Statistics 13, 262–271.
Ericson, W. A. (1969), “Subjective Bayesian models in sampling finite populations” (with discussion). Journal of the Royal Statistical Society, Series B 31, 195–233.
Ericson, W. A. (1970), “On a class of uniformly admissible estimators of a finite population total.” Annals of Mathematical Statistics 41, 1369–1372.
Ghosh, M., and G. Meeden (1983), “Estimation of the variance in finite population sampling.” Sankhya, Series B 45, 362–375.
Ghosh, M., and G. Meeden (1986), “Empirical Bayes estimation in finite population sampling.” Journal of the American Statistical Association. To appear.
Godambe, V. P. (1955), “A unified theory of sampling from finite populations.” Journal of the Royal Statistical Society, Series B 17, 269–278.
Godambe, V. P. (1960), “An admissible estimate for any sampling design.” Sankhya 22, 285–288.
Godambe, V. P. (1966), “Bayes and empirical Bayes estimation in sampling finite populations.” (Abstract). Annals of Mathematical Statistics 37, 552.
Godambe, V. P. (1969), “Admissibility and Bayes estimation in sampling finite populations—V.” Annals of Mathematical Statistics 40, 672–676.
Godambe, V. P., and V. M. Joshi (1965). Joshi (1965), “Admissibility and Bayes estimation in sampling finite populations. I.” Annals of Mathematical Statistics 36, 1707–1722.
Hartley, H. O., and J. N. K. Rao (1968), “A new estimation theory for sample surveys.” Biometrika 55, 547–557.
Joshi, V. M. (1965a), “Admissibility and Bayes estimation in sampling finite populations II.” Annals of Mathematical Statistics 36, 1723–1729.
Joshi, V. M. (1965b), “Admissibility and Bayes estimation in sampling finite populations III.” Annals of Mathematical Statistics 36, 1730–1742.
Joshi, V. M. (1966), “Admissibility and Bayes estimation in sampling finite populations IV.” Annals of Mathematical Statistics 37, 1658–1670.
Joshi, V. M. (1968), “Admissibility of the sample mean as estimate of the mean of a finite population.” Annals of Mathematical Statistics 39, 606–620.
Joshi, V. M. (1969), “Admissibility of estimates of the mean of a finite population.” In New Developments in Survey Sampling, ed. N. L. Johnson and H. Smith, pp. 188 – 212. New York: Wiley-Interscience.
Joshi, V. M. (1970), “Note on the admissibility of the Sen-Yates-Grundy estimator and Murthy’s estimator and its variance estimator for samples of size two.” Sankhya, Series A 32, 431–438.
Joshi, V. M. (1977), “A note on estimators in finite populations.” Annals of Statistics 5, 1051–1053.
Joshi, V. M. (1979), “Joint admissibility of the sample means as estimators of the means of finite populations.” Annals of Statistics 7, 995–1002.
Liu, T. P. (1974), “Bayes estimation for the variance of a finite population.” Metrika 21, 127–132.
Liu, T. P., and M. E. Thompson (1983), “Properties of estimators of quadratic finite population functions: the batch approach.” Annals of Statistics 11, 275–285.
Mazlom, R. I. (1984), “Admissibility in choosing between experiments with applications.” Ph.D. Thesis, Iowa State University.
Mazlom, R. I., and G. Meeden (1986), “Using the stepwise Bayes technique to choose between experiments.” Annals of Statistics. To appear.
Meeden, G., and M. Ghosh (1981), “Admissibility in finite problems.” Annals of Statistics 9, 846–852.
Meeden, G., and M. Ghosh (1983), “Choosing between experiments: applications to finite population sampling.” Annals of Statistics 11, 296–305.
Meeden, G., and M. Ghosh (1984), “On the admissibility and uniform admissibility of ratio type estimators.” In Statistics: Applications and New Directions, ed. J. K. Ghosh and J. Roy, pp. 378 – 390. Calcutta: Indian Statistical Institute.
Meeden, G., M. Ghosh, and S. Vardeman (1985), “Some admissible nonparametric and related finite population sampling estimators.” Annals of Statistics 13, 811–817.
Ramakrishnan, M. K. (1975), “Choice of an optimum sampling strategy—I.” Annals of Statistics 3, 669–679.
Roy, J., and I. M. Chakravarti (1960), “Estimating the mean of a finite population.” Annals of Mathematical Statistics 31, 392–398.
Royall, R. M. (1968), “An old approach to finite population sampling theory.” Journal of the American Statistical Association 63, 1269–1279.
Royall, R. M. (1970), “On finite population sampling theory under certain linear regression models.” Biometrika 57, 377–387.
Scott, A. J. (1975), “On admissibility and uniform admissibility in finite population sampling.” Annals of Statistics 3, 489–491.
Sekkappan, Rm., and M. E. Thompson (1975), “On a class of uniformly admissible estimators for finite populations.” Annals of Statistics 3, 492–499.
Sen, A. R. (1953), “On the estimate of the variance in sampling with varying probabilities.” Journal of the Indian Society of Agricultural Statistics 5, 119–127.
Tsui, K. W. (1983), “A class of admissible estimators of a finite population total.” Annals of the Institute of Statistical Mathematics, Part A 35, 25–30.
Vardeman, S., and G. Meeden (1983a), “Admissible estimators in finite population sampling employing various types of prior information.” Journal of Statistical Planning and Inference 7, 329–341.
Vardeman, S., and G. Meeden (1983b), “Admissible estimators of the population total using trimming and Winsorization.” Statistics and Probability Letters 1, 317–321.
Vardeman, S., and G. Meeden (1984), “Admissible estimators for the total of a stratified population that employ prior information.” Annals of Statistics 12, 675–684.
Yates, F., and P. M. Grundy (1953), “Selection without replacement from within strata with probability proportional to size.” Journal of the Royal Statistical Society, Series B 15, 253–261.
Zacks, S., and H. Solomon (1981), “Bayes and equivariant estimators of the variance of a finite population: Part I, simple random sampling.” Communications in Statistics A, Theory and Methods 10, 407–426.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1987 D. Reidel Publishing Company, Dordrecht, Holland
About this chapter
Cite this chapter
Ghosh, M. (1987). On Admissibility and Uniform Admissibility in Finite Population Sampling. In: MacNeill, I.B., Umphrey, G.J., Bellhouse, D.R., Kulperger, R.J. (eds) Advances in the Statistical Sciences: Applied Probability, Stochastic Processes, and Sampling Theory. The University of Western Ontario Series in Philosophy of Science, vol 34. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4786-3_15
Download citation
DOI: https://doi.org/10.1007/978-94-009-4786-3_15
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-8622-6
Online ISBN: 978-94-009-4786-3
eBook Packages: Springer Book Archive