In the present paper, we develop Lévy-based error prediction in circular systematic sampling. We use a model-based statistical setting as in Hobolth and Jensen (2002), but relax the assumption that the measurement function is Gaussian. The measurement function is represented as a periodic stationary stochastic process X obtained by a kernel smoothing of a Lévy basis. The process X may have an arbitrary covariance function. The distribution of the error predictor, based on measurements in n systematic directions is derived. Statistical inference is developed for the model parameters in the case where the covariance function follows the celebrated p-order covariance model.

Keywords: Fourier series; Lévy basis; planar particles; saddlepoint approximation; stationary stochastic processes; stereology; systematic sampling