ENVIRONMETRICS Environmetrics 2005; 16: 61–69 Published online 15 November 2004 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/env.671 Bias correction for histogram estimator using line transect sampling Omar M. Eidous* ,y Department of Statistics, Faculty of Science, Yarmouk University, Irbid, Jordan SUMMARY This article proposes a simple approach for reducing the bias of the traditional histogram estimator using line transect sampling. The approach uses the bias correction technique, which produces a new estimator for density of objects D. The proposed estimator reduces the bias from Oðh 2 Þ to Oðh 3 Þ as h ! 0 under the shoulder condition assumption. The asymptotic properties of the proposed estimator are derived under some mild assumptions, and the optimal formula for the bin width is given. Small-sample properties of the proposed estimator are studied and compared with some other existence estimators by using a simulation technique. The results show that improve- ments over the traditional histogram estimator often can be realized even at small or moderate sample size. Copyright # 2004 John Wiley & Sons, Ltd. key words: line transect sampling; histogram estimator; bias correction; shoulder condition; half-normal model 1. INTRODUCTION Line transect sampling is an efficient technique for estimating the size of wildlife populations. The populations of interest might be animate or inanimate objects such as animals, birds, trees, etc. (see Burnham et al., 1980). Buckland et al. (1993) provided comprehensive discussions of line transect estimation procedures and assumptions. In the line transect method, an observer attempts to estimate the population density (abundance) D by moving across a study area in lines or transects. The observer counts the number of items detected for each species being investigated and records the perpendicular distance x from the item detected to the path (line) of the observer. When objects are observed from a line transect with detection function gðxÞ, the distance x to the observed object from a randomly placed transect will tend to have a probability density function f ðxÞ of the same shape as gðxÞ but scaled so that the area under f ðxÞ equals unity. Logical considerations deriving from the analysis of the physical sighting process suggest that gðxÞ may usually be assumed monotonically decreasing and satisfying the shoulder condition (i.e. g 0 ð0Þ¼ 0). Accordingly, f ðxÞ is in turn monotonically decreasing with f 0 ð0Þ¼ 0. However, recent studies have shown that the shoulder condition may not hold for some wildlife line transect data such as whales, Received 9 February 2003 Copyright # 2004 John Wiley & Sons, Ltd. Accepted 2 February 2004 *Correspondence to: O. M. Eidous, Department of Statistics, Faculty of Science, Yarmouk University, Irbid, Jordan. y E-mail: omar_eidous@hotmail.com