Development of parametric model for ungrouped and grouped line transect data - Gamil Abdulraqeb, Abdullah Saeed (2021)
Line transect sampling is a frequentist statistical method used in ecology to estimate the population abundance or density of objects in an interested study area. This thesis provides a new method for generating a new detection function based on the line transect sampling theory. The feature of the presented method provides a flexible and automatically monotonic non-increasing model. Based on this method, a new parametric model is developed to estimate the population density based on the line transect data. The advantages of the proposed model are to be strictly monotonically decreasing with perpendicular distance and it satisfies the shoulder condition assumption. Some statistical properties of the proposed model are presented and inference about the estimator f(0) is obtained by considering the method of moments estimation (MME), maximum likelihood estimator (MLE) and the asymptotic distribution for the proposed model are also considered. There are mainly two ways to estimate the population density which are parametric and non-parametric estimation methods. This thesis focus on using the maximum likelihood estimator (MLE) to estimate the parameter of f(0) as the parametric estimation method. For non-parametric estimation methods, a non-parametric kernel is used to propose new estimator for f(0) by combining the kernel estimator with the proposed model. The use of kernel estimator together with the proposed model to compute the smoothing parameter of the kernel estimator is also considered. The performance of the proposed estimator for the developed model is estimated and evaluated using a parametric and non-parametric estimation method via a simulation study and is later compared to existing models in the literature. The developed model is measured by evaluating the performance of the proposed estimators in terms of Relative Mean Error (RME) and the Relative Bias (RB). The results of the simulation study of estimation methods show promising statistical properties of the proposed model which out-performed the existing models. The good performances of the proposed model led to the use of it as a reference to compute the smoothing parameter of the non-parametric kernel estimator. The simulation results also show that the superiority of using the proposed model as a reference over the recommended half-normal model in most considered cases. Finally, both the grouped and ungrouped data are also considered whereby a numerical example using real data is used to illustrate and discuss and has been analysed using the developed model. In addition, the developed model is evaluated based on the variance of the estimators f(0), it is found that the proposed estimator appears to fit data better than the other considered models with the lowest values of variance of f(0) for all cases considered.