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

Abstract

The problem of estimating ( ) f 0 ; the probability density function of observed distances at the left boundary 0 x = using line transect data is considered. A general nonparametric histogram estimator ( ) f 0 t for ( ) f 0 is proposed and investigated. The proposed estimator is formulated as linear of indicator functions with corresponding weights. These weights can be determined in a variety of different ways to ensure desirable properties for the proposed estimator and to deal with the presence or absence of the shoulder condition assumption. Theoretical motivation is provided for the existence of weights that prove to be effective in reducing the bias without increasing variance. We consider a direct implementation of the proposed estimator in which the weights are optimized subject to some constraints. The optimization problem converts into the problem of solving a system of linear equations. Some comparison performances are obtained, which demonstrate the good results of the proposed estimator at least for adequately large samples.

A New Detection Function Model for Distance Sampling Based on the Burr XII Model

“…, X n , with sample sizes of n = 50, 100, 200, 300 and 500. These detection functions were chosen based on the requirement that they depict the many shapes that might appear in the specific field (see Eidous [22]). Target models for simulating perpendicular distances include:…”

“…A comprehensive discussion of line transect sampling can be found in Buckland et al [20], Barabesi et al [21], Eidous et al [22], Eidous et al [23], Jang et al [24], Seber et al [25], Pollock et al [5], Strindberg et al [26], Eberhardt et al [9], Quang et al [27], and Drummer et al [28]. The practical and statistical aspects with line transect sampling are covered in-depth in Burnham and Anderson [29], Routledge and Fyfe [30], Southwell [31], Southwell et al [32], Brockelman et al [33], Drummer et al [28], Chen et al [34], Melville et al [35], and Thomas et al [36].…”

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.…”