Pharmacokinetic studies are commonly analyzed using a two-stage approach where the first stage involves estimation of pharmacokinetic parameters for each subject separately and the second stage uses the individual parameter estimates for statistical inference. This two-stage approach is not applicable in sparse sampling situations where only one sample is available per subject. Nonlinear models are often applied to analyze pharmacokinetic data assessed in such serial sampling designs. Modelling approaches are suitable provided that the form of the true model is known, which is rarely the case in early stages of drug development. This paper presents an alternative approach to estimate pharmacokinetic parameters based on non-compartmental and asymptotic theory in the case of serial sampling when a drug is given as an intravenous bolus. The statistical properties of the estimators of the pharmacokinetic parameters are investigated and evaluated using Monte Carlo simulations.