Performance of Fourier Series is assessed for density estimation problems involving the line transect census method. Simu lated populations of objects characterized by various distributions (Poisson, aggre gated, and uniform) are gener ated to examine important stochastic variables, including detection function, sample size, object movement, and several kinds of observer measurement errors. Circumstances are identified where FS performance is generally acceptable and where alternate models should be sought.
Ambramsky, Z. and G.M. Van Dyne.1980. Field studies and a simulation model of small mammals inhabiting a patchy environment. Oikos35:80-92.
2.
Buckland, S.T.1982. A note on the Fourier Series model for analysing line transect data. Biometrics38: 469-477.
3.
Burnham, K.P. and D.R. Anderson.1976. Mathematical models for nonparametric inferences from line transect data. Biometrics32:325-336.
4.
Burnham, K.P., D.R. Anderson, and J.L. Laake.1980. Estimation of density from line transect sampling of biological populations. Wildlife Monograph72:1-202.
5.
Crain, B.R., K.P. Burnham, D.R. Anderson, and J.L. Laake.1978. A Fourier Series estimator of population density for line transect sampling. Utah State Univ. Press .
6.
Diggle, P.J., J.E. Besag, and J.T. Gleaves.1976. Statistical analysis of spatial point patterns by means of distance methods. Biometrics32:659-667.
7.
Drummer, T.D. and L.L. McDonald.1987. Size bias in line transect sampling . Biometrics43:13-21.
8.
Franzreb, K.E.1981. The determination of avian densities using the variable-strip and fixed-width transect surveying methods. Studies in Avian Biology6:139-145.
9.
Gates, C.E.1969. Simulation study of estimators for the line transect sampling method. Biometrics25:317-328.
10.
Hobson, R.1976. Properties preserved by some smooth functions. Journal American Statistical Assoc.71:763-766.
11.
Johnson, M.E.1987. Multivariate Statistical Simulation. John Wiley and Sons, New York.
12.
Kranz, T.M.1973. Simulation study of the Hahn estimator for estimating deer population density. M.S. thesis, Texas A&M University .
13.
Kronmal, R. and M. Tarter.1968. The estimation of probability densities and cumulatives by Fourier Series methods. Journal American Statistical Assoc.63:925-952.
14.
Pickford, S.G. and J.W. Hazard.1978. Simulation studies on line intersect sampling of forest residue. Forest Science24:469-483.
15.
Pinkowski, B.1988. Heuristic algorithms for clustering spatial-temporal patterns . pp. 635-640 in Proceedings 1988 Summer Computer Simulation Conference , Society for Computer Simulation International.
16.
Quinn, T.J. II.1985. Line transect estimators for schooling populations. Fisheries Research3:183-199.
17.
Rao, P.V.1984. Density estimation based on line transect samples. Statistics and Probability Letters2:51-57.
18.
Smith, G.E.J.1979. Some aspects of line transect sampling when the target population moves. Biometrics35:323-329.
19.
Tanenbaum, A.S.1988. Computer Networks. Prentice-Hall, Englewood Cliffs, New Jersey.
20.
Tarter, M.E. and R.A. Kronmal.1967. A description of new computer methods for estimating the population density. Proceedings of the ACM22:511-519.
21.
Tarter, M.E. and R.A. Kronmal.1976. An introduction to the implementation and theory of nonparametric density estimation. American Statistician30:105-112.
22.
Vandermeer, J.1981. Elementary Mathematical Ecology. John Wiley & Sons, New York.
23.
Wegman, E.J.1972a. Non-parametric probability density estimation. I. A summary of available methods. Technometrics14:533-546.
24.
Wegman, E.J.1972b. Non-parametric probability density estimation. II. A comparison of density estimation methods. J. Statistical Computation and Simulation1: 225-245.
