TY - JOUR
T1 - Kernel estimation in transect sampling without the shoulder condition
AU - Mack, Y. P.
AU - Quang, Pham X.
AU - Zhang, Shunpu
PY - 1999
Y1 - 1999
N2 - We consider the estimation of wildlife population density based on line transect data. Nonparametric kernel method is employed, without the usual assumption that the detection curve has a shoulder at distance zero, with the help of a special class of kernels called boundary kernels. Asymptotic distribution results are included. It is pointed out that the boundary kernel of Zhang and Karunamuni (1998) (see also Müller and Wang (1994)) performs better (for asymptotic mean square error consideration) than that of the boundary kernel of Müller (1991). But both of these kernels are clearly superior to the half-normal and one-sided Epanechnikov kernel when the shoulder condition fails to hold. In practice, however, for small to moderate sample sizes, caution should be exercised in using boundary kernels in that the density estimate might become negative. A Monte Carlo study is also presented, comparing the performance of four kernels applied to detection data, with and without the shoulder condition. Two boundary kernels for derivatives arc also included for the point transect case.
AB - We consider the estimation of wildlife population density based on line transect data. Nonparametric kernel method is employed, without the usual assumption that the detection curve has a shoulder at distance zero, with the help of a special class of kernels called boundary kernels. Asymptotic distribution results are included. It is pointed out that the boundary kernel of Zhang and Karunamuni (1998) (see also Müller and Wang (1994)) performs better (for asymptotic mean square error consideration) than that of the boundary kernel of Müller (1991). But both of these kernels are clearly superior to the half-normal and one-sided Epanechnikov kernel when the shoulder condition fails to hold. In practice, however, for small to moderate sample sizes, caution should be exercised in using boundary kernels in that the density estimate might become negative. A Monte Carlo study is also presented, comparing the performance of four kernels applied to detection data, with and without the shoulder condition. Two boundary kernels for derivatives arc also included for the point transect case.
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U2 - 10.1080/03610929908832422
DO - 10.1080/03610929908832422
M3 - Article
AN - SCOPUS:0042110195
SN - 0361-0926
VL - 28
SP - 2277
EP - 2296
JO - Communications in Statistics - Theory and Methods
JF - Communications in Statistics - Theory and Methods
IS - 10
ER -