Survey Methodology
Adaptive rectangular sampling: An easy, incomplete, neighbourhood-free adaptive cluster sampling design

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by Bardia PanahbehaghNote 1

  • Release date: December 20, 2016
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Abstract

This paper introduces an incomplete adaptive cluster sampling design that is easy to implement, controls the sample size well, and does not need to follow the neighbourhood. In this design, an initial sample is first selected, using one of the conventional designs. If a cell satisfies a prespecified condition, a specified radius around the cell is sampled completely. The population mean is estimated using the π ‑ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipC0xd9Wqpe0dd9 qqaqFeFr0xbbG8FaYPYRWFb9fi0lXxbvc9Ff0dfrpm0dXdHqps0=vr 0=vr0=fdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiWdahcba Gaa8xRaaaa@393E@ estimator. If all the inclusion probabilities are known, then an unbiased π ‑ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipC0xd9Wqpe0dd9 qqaqFeFr0xbbG8FaYPYRWFb9fi0lXxbvc9Ff0dfrpm0dXdHqps0=vr 0=vr0=fdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiWdahcba Gaa8xRaaaa@393E@ estimator is available; if, depending on the situation, the inclusion probabilities are not known for some of the final sample units, then they are estimated. To estimate the inclusion probabilities, a biased estimator is constructed. However, the simulations show that if the sample size is large enough, the error of the inclusion probabilities is negligible, and the relative π ‑ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrpipC0xd9Wqpe0dd9 qqaqFeFr0xbbG8FaYPYRWFb9fi0lXxbvc9Ff0dfrpm0dXdHqps0=vr 0=vr0=fdbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiWdahcba Gaa8xRaaaa@393E@ estimator is almost unbiased. This design rivals adaptive cluster sampling because it controls the final sample size and is easy to manage. It rivals adaptive two-stage sequential sampling because it considers the cluster form of the population and reduces the cost of moving across the area. Using real data on a bird population and simulations, the paper compares the design with adaptive two-stage sequential sampling. The simulations show that the design has significant efficiency in comparison with its rival.

Key Words:  Adaptive cluster sampling; Adaptive two-stage sequential sampling; Primary and secondary sampling units; Inclusion probability.

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How to cite

Panahbehagh, B. (2016). Adaptive rectangular sampling: An easy, incomplete, neighbourhood-free adaptive cluster sampling design. Survey Methodology, Statistics Canada, Catalogue No. 12-001-X, Vol. 42, No. 2. Paper available at http://www.statcan.gc.ca/pub/12-001-x/2016002/article/14684-eng.htm.

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ISSN : 1492-0921

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© Minister of Industry, 2016

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Catalogue No. 12-001-X

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