Model‐based estimator of total expenditure on environmental protection

Abstract

Expenditure of enterprises on environmental protection has highly positive or zero values. Thus, distribution of such a variable is skewed, and its population variance is high. As a consequence the design‐based estimator of a total expenditure has a high variance. The censored regression model (tobit model) for transformed study variable is used in this paper. The values of the study variable of non‐sampled elements are estimated using this model, and a new estimator of the total expenditure is obtained. In the case of simple random sampling and known model parameters, it is shown by simulation that the empirical mean square error of such a model‐based estimator is lower than that of the design‐based one. Due to estimation of the unknown model parameters the mean square error of the estimator is higher.

Key words:

• finite population
• model‐based estimator of a total
• tobit model