LÉVY-BASED ERROR PREDICTION IN CIRCULAR SYSTEMATIC SAMPLING

Kristjana Ýr Jónsdóttir, Eva B. Vedel Jensen

Abstract

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.

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

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DOI: 10.5566/ias.v32.p117-125

Image Analysis & Stereology
EISSN 1854-5165 (Electronic version)
ISSN 1580-3139 (Printed version)