In this
paper, a regression method of estimation has been used to derive the mean
estimate of the survey variable using simple random sampling without replacement in the presence of observational
errors. Two covariates were used and a case where the observational
errors were in both the survey variable and the covariates was considered. The
inclusion of observational errors was due to the fact that data collected
through surveys are often not free from errors
that occur during observation. These errors can occur due to over-reporting, under-reporting, memory failure by the respondents or use of imprecise tools of
data collection. The expression of mean squared error (MSE) based on the
obtained estimator has been derived to the first degree of approximation. The
results of a simulation study show that the derived modified regression mean
estimator under observational errors is more efficient than the mean per unit
estimator and some other existing estimators. The proposed estimator can
therefore be used in estimating a finite population mean, while considering
observational errors that may occur during a study.
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