Precision of stereological planar area predictors

Journal of Microscopy

Volumn 222, Issue 3, 2006, Pages 201-211

  Kiêu, Kiên ^a   Mora, Marianne ^b  

^a UR341 National Agronomical Research Institute (INRA)   (France)

^b UNIVERSITÉ PARIS OUEST NANTERRE LA DÉFENSE   (France)

Author keywords

Area estimation; Covariogram; Lattice; Mean squared error; Power spectral density; Stereology; Stochastic geometry; Systematic sampling

Indexed keywords

ERRORS; POWER SPECTRAL DENSITY; STOCHASTIC SYSTEMS;

AREA ESTIMATION; COVARIOGRAM; LATTICE; LINE-SEGMENTS; MEAN SQUARED ERROR; POINT PATTERNS; SAMPLING SCHEMES; STEREOLOGY; STOCHASTIC GEOMETRY; SYSTEMATIC SAMPLING;

MEAN SQUARE ERROR;

CONFERENCE PAPER; ERROR; MATHEMATICAL ANALYSIS; PREDICTION; PRIORITY JOURNAL; SAMPLING; SIMULATION; STEREOLOGY;

EID: 33745823145     PISSN: 00222720     EISSN: 13652818     Source Type: Journal    
DOI: 10.1111/j.1365-2818.2006.01588.x     Document Type: Conference Paper

References (21)

1. Baddeley, A.J. & Cruz-Orive, L.M. (1995) The Rao-Blackwell theorem in stereology and some counterexamples. Adv. Appl. Probab. 27, 2-19.
2. Byrd, R.H., Lu, P., Nocedal, J. & Zhu, C. (1995) A limited memory algorithm for bound constrained optimization. SIAM J. Sci. Comput. 16, 1190-1208.
3. Chowla, S. & Selberg, A. (1949) On Epstein's zeta function (I). Proc. Acad. Sci. USA, 35, 371-374.
4. Conway, J. & Sloane, N., eds. (1999) Sphere Packings, Lattices and Groups. Springer-Verlag, New York.
5. Crandall, R.E. (1998) Fast evaluation of Epstein zeta functions. URL http://www.perfsci.com/free/techpaper/epstein.pdf.
6. Cruz-Orive, L.M. (1989) On the precision of systematic sampling: a review of Matheron's transitive methods. J. Microsc. 153, 315-333.
7. Gual Arnau, X. & Cruz-Orive, L.M. (1998) Variance prediction under systematic sampling with geometric probes. Adv. Appl. Probab. 28, 982-992.
8. Gundersen, H.J.G. & Jensen, E.B. (1987) The efficiency of systematic sampling in stereology and its prediction. J. Microsc. 147, 229-263.
9. Jensen, E.B. & Gundersen, H.J.G. (1981) Stereological ratio estimation based on counts from integral test systems. J. Microsc. 125, 51-66.
10. Kellerer, A.M. (1989) Exact formulae for the precision of systematic sampling. J. Microsc. 153, 285-300.
11. Kendall, D.G. (1948) On the number of lattice points inside a random oval. Q. J. Math. Oxford Ser. 19, 1-26.
12. Kendall, D.G. & Rankin, R. (1953) On the number of points of a given lattice in a random hypersphere. Q. J. Math. Oxford. Ser. 4, 178-189.
13. Kiêu, K. & Mora, M. (2004) Asymptotics for geometric spectral densities and a stochastic approach of the lattice-point problem. Mathematicae Notae XLII, 77-93.
14. Kiêu, K. & Mora, M. (2005) Stereological Estimation of Mean Volume: Precision of Three Simple Sampling Designs. Technical Report 2005-1. Unité de Mathématiques et informatique appliquées, INRA, Domaine de Vilvert, Jouy-en-Josas.
15. Matérn, B. (1985) Estimating area by dot counts. Contributions to Probability and Statistics in Honour of Gunnar Blom (ed. by J. Lanke and G. Lindgren), pp. 243-257. Department of Mathematical Statistics, University of Lund.
16. Matérn, B. (1989) Precision of area estimation: a numerical study. J. Microsc. 153, 269-284.
17. Matheron, G. (1971) The Theory of Regionalized Variables and its Applications. Technical Report. Centre de morphologie mathématique, Ecole des mines de Paris, Paris.
18. Matheron, G. (1975) Random Sets and Integral Geometry. John Wiley & Sons, New-York.
19. Matheron, G. (1993) Une conjecture sur la covariance d'un ensemble aléatoire. Cahiers de Géostatistiques Fasc. 3. Ecole des Mines de Paris, Paris.
20. Rankin, R.A. (1953) A minimum problem for the Epstein zeta function. Proc. Glasgow Math. Assoc. 1, 149-158.
21. Schlather, M. (2001) Simulation and analysis of random fields. R. News, 1, 18-20.