New variance expressions for systematic sampling: the filtering approach

Authors

  • XIMO GUAL-ARNAU,

    1. Department of Mathematics, Campus Riu Sec, University Jaume I, E-12071 Castellon, Spain
      *Department of Mathematics, Statistics and Computation, Faculty of Sciences, University of Cantabria, Avda. Los Castros s/n, E-39005 Santander, Spain
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  • and * LUIS M. CRUZ-ORIVE

    1. Department of Mathematics, Campus Riu Sec, University Jaume I, E-12071 Castellon, Spain
      *Department of Mathematics, Statistics and Computation, Faculty of Sciences, University of Cantabria, Avda. Los Castros s/n, E-39005 Santander, Spain
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Luis M. Cruz–Orive. Tel: +34 942 20 14 24; fax: +34 942 20 14 02; e-mail: Lcruz@matesco.unican.es

Summary

We present a collection of variance models for estimators obtained by geometric systematic sampling with test points, quadrats, and n-boxes in general, on a bounded domain in n-dimensional Euclidean space ℝn, n = 1, 2, ... , and for systematic rays and sectors on the circle. The approach adopted − termed the filtering approach − is new and different from the current transitive approach. This report is only preliminary, however, because it includes only variance models in terms of the covariogram of the measurement function. The estimation step is in preparation.

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