A Simple Variance Estimator for Unequal Probability Sampling without Replacement

References

• Andersson , C and Nordberg , L . 1994 . A method for variance estimation of non-linear function of totals in surveys . Journal of Official Statistics , 10 : 396 – 405 .
   Google Scholar
• Berger , YG . 1998 . Rate of convergence for asymptotic variance for the Horvitz–Thompson estimator . Journal of Statistical Planning and Inference , 74 : 149 – 168 .
   Web of Science ®Google Scholar
• Berger , YG . 2003a . A modified Hájek variance estimator for systematic sampling . Statistics in Transition, Polish Statistical Association , 6 : 5 – 21 .
   Google Scholar
• Berger YG 2003b Variance estimation for systematic sampling with unequal probabilities under fixed ordering of a population SSRC Working Papers Series, Southampton paper submitted
   Google Scholar
• Brewer KRW 2002 Combined Survey Sampling Inference (Weighing Basu’s Elephants) London: Arnold
   Google Scholar
• Chao , MT . 1982 . A general purpose unequal probability sampling plan . Biometrika , 69 : 653 – 656 .
   Web of Science ®Google Scholar
• Connor , WS . 1966 . An exact formula for the probability that two specified sample units will occur in a sample drawn with unequal probabilities and without replacement . Journal of the American Statistical Association , 61 : 384 – 390 .
   Google Scholar
• Dalenius , T and Hodges , JL . 1959 . Minimum variance stratification . Journal of the American Statistical Association , 54 : 88 – 101 .
   Web of Science ®Google Scholar
• Department of Social Security 2001 Households Below Average Income 1999/00 Appendix 2: Methodology
   Google Scholar
• Deville , JC . 1999 . Variance estimation for complex statistics and estimators: linearization and residual techniques . Survey Methodology , 25 : 193 – 203 .
   Google Scholar
• Gabler , S . 1984 . On unequal sampling: sufficient conditions for the superiority of sampling without replacement . Biometrika , 71 : 171 – 175 .
   Web of Science ®Google Scholar
• Hájek , J . 1964 . Asymptotic theory of rejective sampling with varying probabilities from a finite population . Annal of Mathematical Statistics , 35 : 1491 – 1523 .
   Google Scholar
• Hájek J 1981 Sampling from a Finite Population New York: Marcel Dekker
   Google Scholar
• Hansen , MH and Hurwitz , WN . 1943 . On the theory of sampling from finite population . Annal of Mathematical Statistics , 14 : 333 – 362 .
   Google Scholar
• Hartley , HO and Rao , JNK . 1962 . Sampling with unequal probabilities and without replacement . Annal of Mathematical Statistics , 33 : 350 – 374 .
   Google Scholar
• Hidiroglou , MA and Gray , GB . 1980 . Construction of joint probability of selection for systematic pps sampling . Applied Statistics , 29 : 107 – 112 .
   Google Scholar
• Horvitz , DG and Thompson , DJ . 1952 . A generalization of sampling without replacement from a finite universe . Journal of the American Statistical Association , 47 : 663 – 685 .
   Web of Science ®Google Scholar
• Narain , RD . 1951 . On sampling without replacement with varying probabilities . Journal of the Indian Society of Agricultural Statistics , 3 : 169 – 174 .
   Google Scholar
• Pinciaro SJ 1978 An algorithm for calculating joint inclusion probabilities under PPS systematic sampling ASA Proceedings of Survey Research Methods Section, p. 740
   Google Scholar
• Rao , JNK . 1965 . On two simple schemes of unequal probability sampling without replacement . Journal of the Indian Statistical Association , 3 : 173 – 180 .
   Google Scholar
• Rosén B 1991 Variance for systematic pps-sampling Report 1991:15, Statistics Sweden
   Google Scholar
• Sampford , MR . 1967 . On sampling without replacement with unequal probabilities of selection . Biometrika , 54 : 494 – 513 .
   Web of Science ®Google Scholar
• Särndal CE Swenson B Wretman JH 1992 Model Assisted Survey Sampling Springer-Verlag
   Google Scholar
• Sen , PK . 1953 . On the estimate of the variance in sampling with varying probabilities . Journal of the Indian Society of Agricultural Statistics , 5 : 119 – 127 .
   Google Scholar
• Skinner CJ 1989 In: C. J. Skinner, D. Holt & T. M. F. Smith (Eds) Analysis of Complex Surveys Chichester: Wiley
   Google Scholar
• Smith , TMF . 2001 . Biometrika centenary: sample surveys . Biometrika , 88 : 167 – 194 .
   Web of Science ®Google Scholar
• Yates , F and Grundy , PM . 1953 . Selection without replacement from within strata with probability proportional to size . Journal of the Royal Statistical Society Series B , 1 : 253 – 261 .
   Google Scholar