Journal of Statistics Applications & Probability

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This paper provides insights to researchers when conducting a survey and the response rate is very low, and it is of interest to increase response rate and to estimate the optimal population mean. The paper considers a population that consists of two strata, respondents, and non-respondents. The sampling design is to select a random sample of size n, then when only r observations respond to the survey, select an optimal random sample of size m that minimizes the expected loss, from the remaining (n-r) observations. A truncated Bayesian approach sampling plan is considered [1], such that the posterior distribution of the first stage is treated as a prior to the second stage, and an over-all mean is estimated. The paper illustrates Ericson approach to two random data sets with two sets of priors where the estimated overall mean is obtained for each stage and the expected loss is computed for the two prior sets. It is concluded that priors on means affect the optimal estimate for the mean; under the selected two priors, the final covariance matrix is approximately the same, and the losses are approximately equal when the r responses are more than 20%.

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