• Proceedings of the Korean Statistical Society Conference
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• 2005.05a
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• pp.233-238
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• 2005

S${\"{a}}$rndal (1996) and Knottnerus (2003) had a critical look at the well known variance estimator of Sen (1953) and Yates and Grundy (1953) in probability proportional to size sampling. In this paper, we point out that although their approaches can avoid the difficulties in variance estimation with respect to the joint probabilities, there exist the disadvantages in practice. Also, we describe a sampling procedure available in statistical software that are useful for the variance estimation.

• Communications for Statistical Applications and Methods
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• v.13 no.1
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• pp.61-72
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• 2006

When using the well-known variance estimator of Sen (1953) and Yates and Grundy (1953) in inclusion probability proportional to size sampling, we often encounter the problems due to the calculation of the joint probabilities. Sarndal (1996) and Knottnerus (2003) proposed alternative strategies for variance estimation to avoid those problems in the traditional method. We discuss some of practical issues that arise when they are used. Also, we describe the traditional strategy using a sampling procedure available in a statistical software. It would be one of the attractive choices for design-based variance estimation.

• Communications for Statistical Applications and Methods
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• v.12 no.1
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• pp.181-189
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• 2005

This paper suggest a method of inclusion probability proportional to size sampling that provides a non-negative and stable variance estimator. The sampling procedure is quite simple and flexible since a sampling design is easily obtained using mathematical programming. This scheme appears to be preferable to Nigam, Kumar and Gupta's (1984) method which uses a balanced incomplete block designs. A comparison is made with their method through an example in the literature.