LÉVY-BASED ERROR PREDICTION IN CIRCULAR SYSTEMATIC SAMPLING

• Main Authors: Kristjana Ýr Jónsdóttir, Eva B. Vedel Jensen
• Format: Article
• Language: English
• Published: Slovenian Society for Stereology and Quantitative Image Analysis 2013-06-01
• Series: Image Analysis and Stereology
• Subjects: Fourier series; Lévy basis; planar particles; stationary stochastic processes; stereology; systematic sampling
• Online Access: http://www.ias-iss.org/ojs/IAS/article/view/972
• ISSN: 1580-3139; 1854-5165

In the present paper, Lévy-based error prediction in circular systematic sampling is developed. A model-based statistical setting as in Hobolth and Jensen (2002) is used, but the assumption that the measurement function is Gaussian is relaxed. 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.