Kernel methods in line and point transect sampling

Biometrics

Volumn 54, Issue 2, 1998, Pages 606-619

  Mack, Y P ^a   Quang, Pham X ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF ALASKA FAIRBANKS   (United States)

Author keywords

Asymptotic normality; Kernel method; Line transect sampling; Point transect sampling; Random sample size

Indexed keywords

FOURIER SERIES;

ASYMPTOTIC NORMALITY; KERNEL ESTIMATION; KERNEL-METHODS; LINE TRANSECT SAMPLING; POINT TRANSECT SAMPLING; RANDOM SAMPLE; RANDOM SAMPLE SIZE; SAMPLE SIZES; TRANSECT SAMPLING;

POPULATION STATISTICS;

KERNEL ESTIMATION; POPULATION DENSITY; TRANSECT SAMPLING;

ARTICLE; FOURIER ANALYSIS; POPULATION DENSITY; SAMPLE; UNITED STATES;

EID: 0031745526     PISSN: 0006341X     EISSN: None     Source Type: Journal    
DOI: 10.2307/3109767     Document Type: Article

References (31)

1. Alpizar-Jára, R. and Pollock, K. H. (1996). A combination of line transect and capture-recapture sampling model for multiple observers in aerial surveys. Journal of Ecological and Environmental Statistics 3, 311-327.
2. Anscombe, F. J. (1952). Large-sample theory of sequential estimation. Proceedings of the Cambridge Philosophical Society 48, 600-607.
3. Azari, A. S., Mack, Y. P., and Müller, H. G. (1992). Ultraspherical polynomial, kernel and hybrid estimators for nonparametric regression. Sankhya, Series A 54, 80-96.
4. Buckland, S. T. (1992). Fitting density functions using polynomials. Applied Statistics 41, 63-76.
5. Buckland, S. T. and Turnock, B. J. (1992). A robust line transect method. Biometrics 48, 901-909.
6. Buckland, S. T., Andersen, D. R., Burnham, K. P., and Laake, J. L. (1993). Distance Sampling: Estimating Abundance of Biological Populations. New York: Chapman and Hall.
7. Burnham, K. P. and Anderson, D. R. (1976). Mathematical models for nonparametric inferences from line transect data. Biometrics 32, 325-336.
8. Burnham, K. P., Anderson, D. R., and Laake, J. L. (1980). Estimation of density from line transect sampling of biological populations. Wildlife Monograph 72, supplement to Journal of Wildlife Management 44.
9. Chen, S. X. (1996). Studying school size effects in line transect sampling using the kernel method. Biometrics 52, 1283-1294.
10. Cline, D. B. and Hart, J. D. (1991). Kernel estimation of densities with discontinuities or discontinuous derivatives. Mathematische Operationsforschung und Statistik 22, 69-84.
11. Cressie, N. A. C. (1991). Statistics for Spatial Data. New York: John Wiley and Sons.
12. Drummer, T. D. and McDonald, L. L. (1987). Size bias in line transect sampling. Biometrics 43, 13-21.
13. Gates, C. E., Evans, W., Gober, D. R., Guthery, F. S., and Grant, W. E. (1985). Line transect estimation of animal densities from large data sets. In Game Harvest Management, S. L. Beasom, and S. F. Robeson (eds), 37-50. Kingsville: Caesar Kleberg Research Institute, Texas A&I University.
14. Hardie, W. (1990). Applied Nonparametric Regression. Cambridge: Cambridge University Press.
15. Johnson, E. G. and Routledge, R. D. (1985). The line transect method: A nonparametric estimator based on shape restrictions. Biometrics 41, 669-679.
16. Knopf, F. L., Sedgwick, J. A., and Cannon, R. W. (1988). Guild structure of a riparian avifauna relative to seasonal cattle grazing. Journal of Wildlife Management 52, 280-290.
17. Mack, Y. P. and Müller, H. G. (1987). Adaptive nonparametric estimation of a multivariate regression function. Journal of Multvariate Analysis 23, 169-182.
18. Manly, B. F, McDonald, L. L., and Garner, G. W. (1996). The double count method with two independent observers. Journal of Agricultural, Biological and Environmental Statistics 1, 170-189.
19. Nadaraya, E. A. (1964). On estimating regression. Theory of Probability and Applications 9, 141-142.
20. Quang, P. X. (1991). A nonparametric approach to size-biased line transect sampling. Biometrics 47, 269-279.
21. Quang, P. X. (1993). Nonparametric estimators for variable circular plot surveys. Biometrics 49, 837-852.
22. Quang, P. X. and Becker, E. F. (1996). Line transect sampling under varying conditions with applications to aerial surveys. Ecology 77(4), 1297-1302.
23. Quang, P. X. and Becker, E. F. (1997). Combining line transect and double count sampling techniques for aerial surveys. Journal of Agricultural, Biological and Environmental Statistics 2, 1-14.
24. Ramsey, F. L. and Scott, J. M. (1979). Estimating population densities from variable circular plot surveys. In Sampling Biological Populations, R. M. Cormack, G. P. Patil, and D. S. Robson (eds), 155-181. Fairland, Maryland: International Publishing House.
25. Rosenblatt, M. (1956). Remarks on some nonparametric estimates of a density function. Annals of Mathematical Statistics 27, 642-649.
26. Schuster, E. F. (1972). Joint asymptotic distribution of the estimated regression function at a finite number of distinct points. Annals of Mathematical Statistics 43, 84-88.
27. Schweder, T. (1990). Independent observer experiments to estimate the detection function in line transect surveys of whales. Report of the Internatioanl Whaling Commission 40, 349-355.
28. Seber, G. A. F. (1973). The Estimation of Animal Abundance. New York: Hafner.
29. Silverman, B. W. (1986). Density Estimation for Statistics and Data Analysis. New York: Chapman and Hall.
30. Watson, G. S. (1964). Smooth regression analysis. Sankhya, Series A 26, 383-393.
31. Zahl, S. (1989). Line transect sampling with unknown probability of detection along the transect. Biometrics 45, 453-470.