Variance prediction for pseudosystematic sampling on the sphere

Advances in Applied Probability

Volumn 34, Issue 3, 2002, Pages 469-483

  Gual Arnau, Ximo ^a   Cruz Orive, Luis M ^a  

^a UNIVERSITAT JAUME I   (Spain)

Author keywords

Bernoulli polynomial; Covariogram; Fourier analysis; Geometric sampling; Nucleator; Periodic function; Stereology

Indexed keywords

COMPUTER SIMULATION; FUNCTIONS; MATHEMATICAL MODELS; PROBLEM SOLVING; SPHERES;

PSEUDOSYSTEMATIC SAMPLING; VARIANCE;

RANDOM PROCESSES;

EID: 0036755744     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1239/aap/1033662160     Document Type: Article

References (14)

1. Abramowltz, M. and Stegun, I.A. (1965). Handbook of Mathematical Functions. Dover, New York.
2. Cressie, N.A.C. (1991). Statistics for Spatial Data. John Wiley, New York.
3. Cruz-Orive, L.M. (1989). On the precision of systematic sampling: a review of Matheron's transitive methods. J. Microscopy 153, 315-333.
4. Foley, A., Lane, D.A., Nielson, G.M., Franke, R. and Hagen, H. (1990). Interpolation of scattered data on closed surfaces. Comput. Aided Geometric Design 7, 303-312.
5. García-Fiñana, M. and Cruz-Orive, L.M. (2000). New approximations for the efficiency of Cavalieri sampling. J. Microscopy 199, 224-238.
6. Gual-Arnau, X. and Cruz-Orive, L.M. (2000). Systematic sampling on the circle and on the sphere. Adv. Appl. Prob. 32, 628-647.
7. Gundersen, H.J.G. (1988). The nucleator. J. Microscopy 151, 3-21.
8. Jensen, E.B.V. (1998). Local Stereology. World Scientific, Singapore.
9. Kiêu, K., Souchet, S. and Istas, J. (1999). Precision of systematic sampling and transitive methods. J. Statist. Planning Infer. 77, 263-279.
10. Lockwood, E.H. and Macmillan, R.H. (1978). Geometric Symmetry. Cambridge University Press.
11. Matheron, G. (1971). The Theory of Regionalized Variables and Its Applications (Cahiers Centre Morphologie Math. 5). École des Mines de Paris, Fontainebleau.
12. Riordan, J. (1968). Combinatorial Identities. John Wiley, New York.
13. Schlather, M. (1999). An introduction to positive definite functions and to unconditional simulation of random fields. Tech. Rep. ST 99-10, Lancaster University.
14. Tandrup, T. (1993). A method for unbiased and efficient estimation of number and mean volume of specified neuron subtypes in rat dorsal root ganglion. J. Comparative Neurol. 329, 269-276.