Alternative approach to finite population estimation with many zero values
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Online ISSN 2005-2863 Print ISSN 1226-3192
RESEARCH ARTICLE
Alternative approach to finite population estimation with many zero values Bardia Panahbehagh1 · Jennifer Brown2 Received: 2 March 2019 / Accepted: 29 November 2019 © Korean Statistical Society 2020
Abstract In some sampling situations, the survey can result in an estimate of zero when it is known that the parameter being estimated is close to, but not equal to, zero. Examples include searching for rare animals or plants where the species is known to exist but all sample units failed to detect any activity. One way to deal with this is to ignore these zero estimates. Here we propose an estimator for sampling where we know the parameter of interest is not zero. Our proposed non-zero estimator will improve estimation and it can be more efficient than conventional estimators. Keywords Adaptive cluster sampling · Finite population sampling · Rare population · Unbiased estimator
1 Introduction Estimation of unknown parameters from finite populations is a long standing research field. One of the important advancements in this field was the introduction of π -estimators by Narain (1951) and Horvitz and Thompson (1952) for unequal probabilities sampling designs. In this paper, we are interested in survey situations where the variable of interest in the population can take the value of zero, and as a result, the estimates of the population parameter can itself be zero. This is a problem when the population parameter, for example the total population size, or density per ha, is known to be some value other than zero. Surveys of rare animals and plants are an example where there may have been sign of the rare animal, such as recent foot tracks, indication of recent browsing, or observations of the plant’s leaves or pollen traces. A survey may be undertaken
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Bardia Panahbehagh [email protected]
1
Department of Mathematics, Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran
2
School of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand
123
Journal of the Korean Statistical Society
to estimate the population size, covering an extensive area of the animal or plant’s range, with many sample units. In this example the sample units could be sample plots, transects or quadrats. If all the sample units in the survey return zero values the estimate of the population total would be zero, an estimate that is clearly incorrect. When we know the population parameter is not zero, is there an alternative to accepting zero as an estimate? Zero estimation can be a result of structural zeros or, alternatively, of what can be called, random zeros. Structural zeros are when the variable of interest has a value of zero because there are no other possible values it could be. In the example above, if there were no individuals of the species of interest in the study area, the total of the population is zero and all sample units will have a zero value. Random zeros would be when the total of the population is greate
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