Nonparametric density estimation from biased data with unknown biasing function

Journal of the American Statistical Association

Volumn 95, Issue 451, 2000, Pages 865-876

  Lloyd, Chris J ^a   Jones, M C ^b  

^a Australian Graduate School of Management   (Australia)

^b OPEN UNIVERSITY   (United Kingdom)

Author keywords

Kernel density estimation; Mark recapture; Weighted distribution

Indexed keywords

EID: 2242483924     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1080/01621459.2000.10474278     Document Type: Article

References (24)

1. Buckland, S. T., Anderson, D. R., Burnham, K. P., and Laake, J. L. (1993), Distance Sampling, London: Chapman and Hall.
2. Chao, A. (1989), “Estimating Population Size From Sparse Data in Capture-Recapture Experiments,” Biometrics, 45, 427-438.
3. Chapman, D. G. (1951), “Some Properties of the Hypergeometric Distribution With Applications to Zoological Censuses,” University of California Publications in Statistics, 1, 131-160.
4. Chen, S. X. (1996), “A Kernel Estimate for the Density of a Biological Population by Using Line Transect Sampling,” Applied Statistics, 45, 135-150.
5. Chen, S. X., and Lloyd, C. J. (1999), “A Non-Parametric Approach to the Analysis of Two-Stage Mark Recapture Experiments,” Working Paper 99-018, Australian Graduate School of Management, Sydney.
6. Cox, D. R. (1969), “Some Sampling Problems in Technology,” in New Developments in Survey Sampling, eds. N. L. Johnson and H. Smith, New York: Wiley, pp. 506-527.
7. Fan, J., and Marron, J. S. (1994), “Fast Implementations of Nonparametric Curve Estimators,” Journal of Computational and Graphical Statistics, 3, 35-56.
8. Hastie, T. J., and Tibshirani, R. J. (1990), Generalized Additive Models, London: Chapman and Hall.
9. Jones, M. C. (1991), “Kernel Density Estimation for Length-Biased Data,” Biometrika, 78, 511-519.
10. Jones, M. C. (2000), “Rough-and-Ready Assessment of the Degree and Importance of Smoothing in Bootstrapping,” Statistica Neerlandica, 54,37-46.
11. Lloyd, C. J. (1994), “Efficiency of Martingale Methods in Recapture Studies,” Biometrika, 81, 305-315.
12. Lloyd, C. J. (1996), “Accurate Pivotals From Recapture Experiments With Time Variation,” Biometrika, 83, 700-708.
13. Lloyd, C. J. (1999), “Estimating a Frequency Distribution When the Sampling is Biased,” Communications in Statistic, Part A—Theory and Methods, 28, 1115-1132.
14. Lloyd, C. J., and Jones, M. C. (1998), “Non-Parametric Density Estimation From Biased Data With Unknown Biasing Function,” Research Report 194, University of Hong Kong, Dept, of Statistics and Actuarial Science.
15. Patil, G. P., and Rao, C. R. (1977), “The Weighted Distributions: A Survey of Their Applications,” in Applications of Statistics, ed. P. R. Krishnaiah, Amsterdam: North-Holland, pp. 383-405.
16. Patil, G. P., and Rao, C. R. (1978), “Weighted Distributions and Size-Biased Sampling With Applications to Wildlife Populations and Human Families”, Biometrics, 34, 179-189.
17. Patil, G. P., Rao, C. R., and Zelen, M. (1988), “Weighted Distributions,” in Encyclopedia of Statistical Sciences, Vol. 9, eds. S. Kotz and N. L. Johnson, New York: Wiley, pp. 565-571.
18. Scott, D. W. (1992), Multivariate Density Estimation, New York: Wiley.
19. Seber, G. A. F. (1982), Estimation of Animal Abundance and Related Parameters (2nd ed.), London: Griffin.
20. Simonoff, J. S. (1996), Smoothing Methods in Statistics, New York: Springer.
21. Sun, J., and Woodroofe, M. (1997), “Semi-Parametric Estimates Under Biased Sampling,” Statistica Sinica, 1, 545-575.
22. Vardi, Y. (1982), “Nonparametric Estimation in the Presence of Length Bias,” The Annals of Statistics, 10, 616-620.
23. Wand, M. P., and Jones, M. C. (1995), Kernel Smoothing, London: Chapman and Hall.
24. Yip, S. F., Huggins, R. M., and Lin, D. Y. (1995), “Inference for Capture-Recapture Experiments in Continuous Time With Variable Capture Rates,” Biometrika, 83, 477-483.