A Statistical Distance Approach to Dissimilarities in Ecological Data

Statistical distances allow us to quantify the closeness between two statistical objects. Many distances are important in statistical inference, but can also be used in a wide variety of applications through goodness-of-fit procedures. This dissertation aims to develop useful theory and applications for these types of procedures. Extensive research has already been done for statistical distances in parameter estimation and hypothesis testing. Specifically, there are a large number of distances that can be chosen to minimize the difference between the data and the assumed model. This procedure is known as the minimum distance approach. It was not necessary that the statistical distance be symmetric in parameter estimation but there are many applications in goodness-of-fit testing that require symmetric distance functions. In this paper, one of the main goals is to establish theory for selecting an appropriate symmetric distance when being used in these types of applications. Secondly, we propose a new class of symmetric distances that share the same desirable properties as previously proposed methods. In addition to focusing on symmetric statistical distances, a new method will be proposed for determining whether or not a particular distance is efficient or robust. Lastly, we exhibit the usefulness of our approach through applications in ecology and image processing