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Journal ArticleDOI

Successive Sampling With $p (p \geqq 1)$ Auxiliary Variables

01 Dec 1972-Annals of Mathematical Statistics (Institute of Mathematical Statistics)-Vol. 43, Iss: 6, pp 2031-2034
TL;DR: In this article, a double-sampling multivariate ratio estimate using $p$ auxiliary variates from the matched portion of the sample has been derived and results are presented for some special cases which have practical applications.
Abstract: In successive sampling on two occasions, the theory developed so far aims at providing the optimum estimate by combining (i) a double-sampling regression estimate from the matched portion of the sample and (ii) a simple mean based on a random sample from the unmatched portion of the sample on the second occasion. Theory has been generalized in the present note by using a double-sampling multivariate ratio estimate using $p$ auxiliary variates $(p \geqq 1)$ from the matched portion of the sample. Expressions for optimum matching fraction and of the combined estimate and its error have been derived and results are presented for some special cases which have practical applications.

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Citations
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Journal ArticleDOI
TL;DR: In this paper, the auxiliary information is often available for all units of a finite population and the estimators of the population means on both occasions and the formulae of their MSE (mean squared error) are given.
Abstract: In practical problems, auxiliary information is often available for all units of a finite population. This paper develops sample rotation method relevant to this case. The estimators of the population means on both occasions and the formulae of their MSE (mean squared error) are given. The results are very similar to the usual ones.

95 citations

Journal ArticleDOI
TL;DR: In this article, a chain type difference and regression estimators have been proposed for estimating the population mean at second (current) occasion in the two occasions rotation (successive) sampling.
Abstract: In rotation (successive) sampling, it is common practice to use the information collected on a previous occasion to improve the precision of the estimates at current occasion. The previous information may be in the form of an auxiliary character, the character under study itself, or both. In the present work, information on an auxiliary character, which is readily available on all the occasions, has been used along with the information on study character from the previous and current occasion. Consequently, chain type difference and regression estimators have been proposed for estimating the population mean at second (current) occasion in the two occasions rotation (successive) sampling. The proposed estimators have been compared with sample mean estimator when there is no matching and the optimum estimator, which is the combination of the means of the matched and unmatched portions of the sample at the second occasion. Optimum replacement policy is also discussed. Theoretical results have been justified ...

67 citations


Cites background from "Successive Sampling With $p (p \geq..."

  • ...Sen (1972, 1973) extended his work for several auxiliary variates....

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  • ...Sen ( 1972 1973 ) extended his work for several auxiliary variates....

    [...]

Journal ArticleDOI
TL;DR: In this paper, the problem of estimating population mean on the current (second) occasion using auxiliary information in successive sampling over two occasions is considered, and a class of estimators is defined with its properties.
Abstract: This article considers the problem of estimating population mean on the current (second) occasion using auxiliary information in successive sampling over two occasions. A class of estimators is defined with its properties. It is shown that the estimator envisaged by Singh (2005) is a particular member of the proposed class of estimators. The superiority of the suggested class of estimators is discussed with sample mean estimator when there is no matching, the best combined estimator given in Cochran (1977, p. 346), Sukhatme et al. (1984, p. 249), Singh's (2005) estimator, and Singh and Vishwakarma's (2007) class of estimators. Optimum replacement policy has been discussed. Numerical illustration is also given.

44 citations


Cites background from "Successive Sampling With $p (p \geq..."

  • ...This permits for an improved estimate of population parameters on the second (current) occasion; for instance, see Sen ( 1971 ); ( 1972 )....

    [...]

01 Jan 2009
TL;DR: In this article, two classes of estimators for the population mean of the study character using multi-auxiliary characters with known population means in presence of nonresponse have been proposed.
Abstract: Two classes of estimators for the population mean of the study character using multi-auxiliary characters with known population means in presence of nonresponse have been proposed. The expressions for bias, mean square error and conditions for attaining minimum mean square error of the proposed classes of estimators have been obtained. An empirical study has also been given in support of the problem.

36 citations

Journal ArticleDOI
TL;DR: In this article, a class of estimators of finite population variance in successive sampling was proposed and its properties were analyzed on real populations and moderate sample sizes, and an empirical study was conducted to evaluate the usefulness of the proposed methodology.
Abstract: 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.

34 citations