Confidence intervals in Cavalieri sampling

Journal of Microscopy

Volumn 222, Issue 3, 2006, Pages 146-157

  Garcia Finana M ^a  

^a UNIVERSITY OF LIVERPOOL   (United Kingdom)

Author keywords

Cavalieri estimator; Confidence interval; Efficiency; Measurement function; Probability distribution; Smoothness constant; Stereology; Systematic sampling; Variance

Indexed keywords

ASYMPTOTIC ANALYSIS; FINANCIAL DATA PROCESSING; SAMPLING; STATISTICAL TESTS;

ASYMPTOTIC DISTRIBUTIONS; CAVALIERI ESTIMATOR; CONFIDENCE INTERVAL; DATA SAMPLE; MEASUREMENT FUNCTION; PROBABILITY: DISTRIBUTIONS; SMOOTHNESS CONSTANT; STEREOLOGY; SYSTEMATIC SAMPLING; VARIANCE;

PROBABILITY DISTRIBUTIONS;

ANALYTIC METHOD; BRAIN CORTEX; CAVALIERI ESTIMATOR; CONFERENCE PAPER; CONFIDENCE INTERVAL; DATA ANALYSIS; MATHEMATICAL ANALYSIS; PRIORITY JOURNAL; SAMPLING; STATISTICAL ANALYSIS; STEREOLOGY;

EID: 33745844385     PISSN: 00222720     EISSN: 13652818     Source Type: Journal    
DOI: 10.1111/j.1365-2818.2006.01534.x     Document Type: Conference Paper

References (18)

1. Abramowitz, M. & Stegim, I.A. (1965) Handbook of Mathematical Functions. Dover, New York.
2. Baddeley, A.J. & Jensen, E.V.B. (2005) Stereology for Statisticians. Chapman & Hall/CRC, Boca Raton, FL.
3. Cruz-Orive, L.M. (1989) On the precision of systematic sampling: a review of Matheron's transitive methods. J. Microsc. 153, 315-333.
4. Cruz-Orive, L.M. & García-Fiñana, M. (2005) A review of the article: Comments on the shortcomings of predicting the precision of Cavalieri volume estimates based upon assumed measurement functions, by Edmund Glaser. J. Microsc. 218, 6-8.
5. García-Fiñana, M. & Cruz-Orive, L.M. (2004) Improved variance prediction for systematic sampling on ℝ. Statistics, 38, 243-272.
6. García-Fiñana, M., Cruz-Orive, L.M., Mackay, C., Pakkenberg, B. & Roberts, N. (2003) Comparison of MR imaging against physical sectioning to estimate the volume of human cerebral compartments. NeuroImage, 18, 505-516.
7. Gual Arnau, X. & Cruz-Orive, L.M. (1998) Variance prediction under systematic sampling with geometric probes. Adv. Appl. Prob. 30, 889-903.
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. Kellerer, A.M. (1989) Exact formulae for the precision of systematic sampling. J. Microsc. 153, 285-300.
10. Kiêu, K. (1997) Three Lectures on Systematic Geometric Sampling. Memoirs 13/1997. Department of Theoretical Statistics, University of Aarush.
11. Kiêu, K., Souchet, S. & Istas, J. (1999) Precision of systematic sampling and transitive methods. J. Statist. Plan. Inf. 77, 263-279.
12. Matheron, G. (1965) Les Variables Regionalisees et Leur Estimation. Masson et Cie., Paris.
13. Matheron, G. (1971) The Theory of Regionalized Variables and its Applications. Les Cahiers du Centre de Morphologie Mathematique de Fontainebleau, no. 5. Ecole nationale superieure des mines de Paris, Fontainebleau.
14. Mattfeldt, T. (1989) The accuracy of one-dimensional systematic sampling. J. Microsc. 153, 301-313.
15. Nishimoto, K. (1984) Fractional Calculus. Descartes Press Co, Koriyama.
16. Roberts, N., Garden, A.S., Cruz-Orive, L.M., Whitehouse, G.H. & Edwards, R.H.T. (1994) Estimation of fetal volume by MRI and stereology. Br. J. Radiol. 67, 1067-1077.
17. Snedecor, G.W. & Cochran, W.G. (1989) Statistical Methods. Iowa State University Press, Ames, IA.
18. Souchet, S. (1995) Precision de l'estimateur de Cavalieri. Rapport de stage, DEA de Statistiques et Modeles Aleatoires appliques a la Finance. Universite Paris-VII, Laboratoire de Biometrie, INRA-Versailles.