This book provides a concise and integrated overview of hypothesis testing in four important subject areas, namely linear and nonlinear models, multivariate analysis, and large sample theory. The approach used is a geometrical one based on the concept of projections and their associated idempotent matrices, thus largely avoiding the need to involvematrix ranks. It is shown that all the hypotheses encountered are either linear or asymptotically linear, and that all the underlying models used are either exactly or asymptotically linear normal models. This equivalence can be used, for example, to extend the concept of orthogonality to other models in the analysis of variance, and to show that the asymptotic equivalence of the likelihood ratio, Wald, and Score (Lagrange Multiplier) hypothesis tests generally applies.

This book provides a concise and integrated overview of hypothesis testing in four important subject areas, namely linear and nonlinear models, multivariate analysis, and large sample theory. The approach used is a geometrical one based on the concept of projections and their associated idempotent matrices, thus largely avoiding the need to involvematrix ranks. It is shown that all the hypotheses encountered are either linear or asymptotically linear, and that all the underlying models used are either exactly or asymptotically linear normal models. This equivalence can be used, for example, to extend the concept of orthogonality to other models in the analysis of variance, and to show that the asymptotic equivalence of the likelihood ratio, Wald, and Score (Lagrange Multiplier) hypothesis tests generally applies.

This study concerns the use of distance sampling to estimate the density or abundance of biological populations. Line and point transect sampling are the primary distance methods. Here, lines or points are surveyed in the field and the observer records a distance to those objects of interest that are detected. The sample data are the set of distances of detected objects and any relevant covariates; however, many objects may remain undetected during the course of the survey. Distance sampling provides a way to obtain reliable estimates of density of objects under fairly mild assumptions. Distance sampling is an extension of plot sampling methods where it is assumed that all objects within sample plots are counted. The objective of this book is to provide a comprehensive treatment of distance sampling theory and application. It covers the theory and application of distance sampling with emphasis on line and point transects. Specialized applications are noted briefly, such as trapping webs and cue counts. General considerations are given to the design of distance sampling surveys.