Estimation of population variance in successive sampling

This paper proposes a class of estimators of finite population variance in successive sampling on two occasions and analyzes its properties. Isaki (J Am Stat Assoc 78:117–123, 1983) motivated to consider the problem of estimation of finite population variance in survey sampling, and its extension to the case of successive sampling is much interesting, and the theory developed here will be helpful to those involved in such analysis in future. To our knowledge this is the first attempt made by the authors in this direction. An empirical study based on real populations and moderate sample sizes demonstrates the usefulness of the proposed methodology. In addition, this paper also presents a through review on successive sampling.

[1]  A. R. Sen,et al.  THE USE OF A RATIO ESTIMATE IN SUCCESSIVE SAMPLING , 1975 .

[2]  Sarjinder Singh.  Generalized Calibration Approach for Estimating Variance in Survey Sampling , 2001 .

[3]  R. J. Jessen,et al.  Statistical investigation of a sample survey for obtaining farm facts , 1942 .

[4]  Housila P. Singh,et al.  Successive Sampling Using Auxiliary Information on Both the Occasions , 2001 .

[5]  A. R. Sen.  SOME THEORY OF SAMPLING ON SUCCESSIVE OCCASIONS1 , 1973 .

[6]  H. Cramér.  Mathematical methods of statistics , 1947 .

[7]  J. N. K. Rao,et al.  ROTATION DESIGNS FOR SAMPLING ON REPEATED OCCASIONS , 1964 .

[8]  Housila P. Singh,et al.  A Class of Estimators Using Auxiliary Information for Estimating Finite Population Variance in Presence of Measurement Errors , 2009 .

[9]  Des Raj,et al.  On Sampling Over Two Occasions with Probability Proportionate to Size , 1965 .

[10]  Sarjinder Singh.  Basic Concepts and Mathematical Notation , 2003 .

[11]  D. Singh,et al.  ON TWO‐STAGE SUCCESSIVE SAMPLING , 1969 .

[12]  R. Tailor,et al.  QUANTILE ESTIMATION IN SUCCESSIVE SAMPLING , 2007 .

[13]  Carl-Erik Särndal,et al.  Model Assisted Survey Sampling , 1997 .

[14]  D. Horvitz,et al.  A Generalization of Sampling Without Replacement from a Finite Universe , 1952 .

[15]  Estimation of population mean in successive sampling using information on auxiliary character , 1996 .

[16]  B. D. Tikkiwal.  THEORY OF MULTIPHASE SAMPLING FROM A FINITE OR AN INFINITE POPULATION ON SUCCESSIVE OCCASIONS 1, 21 , 1967 .

[17]  A. R. Sen.  346. Note: Theory and Application of Sampling on Repeated Occasions with Several Auxiliary Variables , 1973 .

[18]  B. D. Tikkiwal.  On the Theory of Classical Regression and Double Sampling Estimation , 1960 .

[19]  A. R. Sen.  Successive Sampling With $p (p \geqq 1)$ Auxiliary Variables , 1972 .

[20]  G. H. Choudhry,et al.  SAMPLING ON TWO OCCASIONS WITH PPSWOR , 2002 .

[21]  C. T. Isaki,et al.  Variance Estimation Using Auxiliary Information , 1983 .

[22]  A Comparison of Two Sampling Procedures with an Application to Successive Sampling , 1970 .

[23]  H. D. Patterson.  Sampling on Successive Occasions with Partial Replacement of Units , 1950 .

[24]  Paul Bratley,et al.  A guide to simulation , 1983 .

[25]  D. Singh,et al.  Estimates in Successive Sampling Using a Multi-Stage Design , 1968 .

[26]  On ratio estimators in two phase sampling under size stratification and estimation over two successive occasions , 1981 .

[27]  M. Rueda Garcia,et al.  Repeated substitution method: The ratio estimator for the population variance , 1996 .

[28]  Wayne A. Fuller.  Use of Auxiliary Information in Estimation , 2009 .

[29]  Fabian Chukwuemenam Okafor.  The theory and application of sampling over two occasions for the estimation of current population ratio , 1992 .

[30]  D. Singh,et al.  Double Sampling for Stratification on Successive Occasions , 1965 .

[31]  Sarjinder Singh,et al.  Advanced Sampling Theory with Applications : How Michael ' selected' Amy Volume I , 2003 .

[32]  F. Yates,et al.  Sampling Methods for Censuses and Surveys , 1950 .

[33]  A. Srivastava,et al.  A comparison of Midzuno-Sen scheme with P.P.S. sampling without replacement and its applicaton to successive sampling , 1972 .