A Semiparametric Model for Line Transect Sampling

Abstract

This paper introduces an appealing semiparametric model for estimating wildlife abundance based on line transect data. The proposed method requires the existence of a parametric model and then improves the estimator using a kernel method. Properties of the resultant estimator are derived and an expression for the asymptotic mean square error (AMSE) of the estimator is given. Minimization of the AMSE leads to an explicit formula for an optimal choice of the smoothing parameter. Small-sample properties of the proposed estimator using the parametric half-normal model are investigated and compared with the classical kernel estimator using both simulations and real data. Numerical results show that improvements over the classical kernel estimator often can be realized even when the true density is far from the half-normal model.

Nonparametric Estimation off(0) Applying Line Transect Data with and without the Shoulder Condition

“…An important note that we have to mention here is that the large value of r may reduce the AMSE of f t (0,r) asymptotically, but it is not necessar- (4) = 16, R 3 (5) = 29 and R 3 (6) = 48 respectively, which clearly give R 4 (4) < R 4 (5) < R 4 (6) . That is and at least for this case, the value R 4 (r) of increases (in its magnitude) as r increases.…”

“…is the p th derivative of f(x) at x 0 = ) is known as the shoulder condition assumption, which is required for most nonparametric density estimation methods to produce a satisfactory estimator for ( ) f 0 (See for example, Chen, 1996;Quang, 1998 andEidous, 2006). This assumption indicates that the detection of object in a narrow region around the transect line is certain.…”

Variable location kernel method using line transect sampling

“…In recent years, researchers have focused their attention on the kernel method. Buckland (1992), Chen (1996), Gerard and Schucany (1999), Mack (2002) and Eidous (2005Eidous ( , 2006) have all applied the kernel method to line transect data.…”

A Weighted Exponential Model for Grouped Line Transect Data

“…There are some parametric models which were proposed to estimate ( ) (See for example, Gates et al, 1968 andAbabned andEidous, 2012). On the other hand, the nonparametric methods to estimate ( ) have been more attention in the last two decates (See Chen, 1996;Eidous 2005aEidous , 2005bEidous , 2006Eidous , 2009Eidous , 2011aEidous , 2011bEidous , 2012Eidous , 2014Eidous , 2015 and Eidous and Al-Shakhatreh, 2011). However, Nonparametric methods can be used when the perpendicular distances are ungrouped, none of these nonparametric methods can be applied when the data are grouped.…”