Generalization of modified systematic sampling and regression estimation for population with a linear trend

선형추세를 갖는 모집단에 대한 변형계통표집의 일반화와 회귀추정법

  • Kim, Hyuk-Joo (Division of Mathematics and Informational Statistics, Wonkwang University) ;
  • Kim, Jeong-Hyeon (Department of Informational Statistics, Wonkwang University)
  • 김혁주 (원광대학교 수학.정보통계학부) ;
  • 김정현 (원광대학교 정보통계학과)
  • Published : 2009.11.30

Abstract

When we wish to estimate the mean or total of a finite population, the numbering of the population units is of importance. In this paper, we have proposed two methods for estimating the mean or total of a population having a linear trend, for the case when the reciprocal of the sampling fraction is an even number and the sample size is an odd number. The first method involves drawing a sample by using a method which is a generalization of Singh et al's (1968) modified systematic sampling, and using interpolation in determining the estimator. The second method involves selecting a sample by modified systematic sampling, and estimating the population parameters by the regression estimation method. Under the criterion of the expected mean square error based on Cochran's (1946) infinite superpopulation model, the proposed methods have been compared with existing methods. We have also made a comparison between the two proposed methods.

References

  1. 김영화, 김기수 (2009). 고객집단별 보험금에 대한 소지역 추정. <한국데이터정보과학회지>, 20, 77-87.
  2. 김혁주(2004). 변형된 계통추출과 최소제곱법을 이용한 모평균 추정. <응용통계연구>, 17, 105-117.
  3. 박종태 (2009). 소지역의 실업률에 대한 상대위험도의 추정에 관한 비교연구. <한국데이터정보과학회지>, 20, 349-356.
  4. Bellhouse, D. R. and Rao, J. N. K. (1975). Systematic sampling in the presence of a trend. Biometrika, 62, 694-697. https://doi.org/10.1093/biomet/62.3.694
  5. Cochran, W. G. (1946). Relative accuracy of systematic and stratified random samples for a certain class of populations. Annals of Mathematical Statistics, 17, 164-177. https://doi.org/10.1214/aoms/1177730978
  6. Kim, H. J. (1998). Estimation of population mean using interpolation in modified systematic sampling. Korean Annals of Mathematics, 15, 217-231.
  7. Madow, W. G. (1953). On the theory of systematic sampling, III. Comparison of centered and random start systematic sampling. Annals of Mathematical Statistics, 24, 101-106. https://doi.org/10.1214/aoms/1177729087
  8. Murthy, M. N. (1967). Sampling theory and methods, Statistical Publishing Society, Calcutta, India.
  9. Sethi, V. K. (1965). On optimum pairing of units. Sankhya, Series B, 27, 315-320.
  10. Singh, D., Jindal, K. K. and Garg, J. N. (1968). On modified systematic sampling. Biometrika, 55, 541-546. https://doi.org/10.1093/biomet/55.3.541
  11. Yates, F. (1948). Systematic sampling. Philosophical Transactions of the Royal Society of London, A, 241, 345-377. https://doi.org/10.1098/rsta.1948.0023