Spatial statistics are useful in subjects as diverse as climatology, ecology, economics, environmental and earth sciences, epidemiology, image analysis and more. This book covers the best-known spatial models for three types of spatial data: geostatistical data (stationarity, intrinsic models, variograms, spatial regression and space-time models), areal data (Gibbs-Markov fields and spatial auto-regression) and point pattern data (Poisson, Cox, Gibbs and Markov point processes). The level is relatively advanced, and the presentation concise but complete.
The most important...
Spatial statistics are useful in subjects as diverse as climatology, ecology, economics, environmental and earth sciences, epidemiology, image anal...
The aim of the book is to introduce basic concepts, main results, and widely applied mathematical tools in the spectral analysis of large dimensional random matrices. The core of the book focuses on results established under moment conditions on random variables using probabilistic methods, and is thus easily applicable to statistics and other areas of science. The book introduces fundamental results, most of them investigated by the authors, such as the semicircular law of Wigner matrices, the Marcenko-Pastur law, the limiting spectral distribution of the multivariate F matrix,...
The aim of the book is to introduce basic concepts, main results, and widely applied mathematical tools in the spectral analysis of large dimension...
Sample data alone never suffice to draw conclusions about populations. Inference always requires assumptions about the population and sampling process. Statistical theory has revealed much about how strength of assumptions affects the precision of point estimates, but has had much less to say about how it affects the identification of population parameters. Indeed, it has been commonplace to think of identification as a binary event - a parameter is either identified or not - and to view point identification as a pre-condition for inference. Yet there is enormous scope for fruitful inference...
Sample data alone never suffice to draw conclusions about populations. Inference always requires assumptions about the population and sampling process...
This is a book on bootstrap and related resampling methods for temporal and spatial data exhibiting various forms of dependence. Like the resam pling methods for independent data, these methods provide tools for sta tistical analysis of dependent data without requiring stringent structural assumptions. This is an important aspect of the resampling methods in the dependent case, as the problem of model misspecification is more preva lent under dependence and traditional statistical methods are often very sensitive to deviations from model assumptions. Following the tremendous success of...
This is a book on bootstrap and related resampling methods for temporal and spatial data exhibiting various forms of dependence. Like the resam pling ...
This book is an attempt to present a unified theory of rare event simulation and the variance reduction technique known as importance sampling from the point of view of the probabilistic theory of large deviations. This framework allows us to view a vast assortment of simulation problems from a single unified perspective. It gives a great deal of insight into the fundamental nature of rare event simulation. Unfortunately, this area has a reputation among simulation practitioners of requiring a great deal of technical and probabilistic expertise. In this text, I have tried to keep the...
This book is an attempt to present a unified theory of rare event simulation and the variance reduction technique known as importance sampling from th...
For over 200 years, practitioners have been developing parametric families of probability distributions for data analysis. More recently, an active development of nonparametric and semiparametric families has occurred. This book includes an extensive discussion of a wide variety of distribution families--nonparametric, semiparametric and parametric--some well known and some not. An all-encompassing view is taken for the purpose of identifying relationships, origins and structures of the various families. A unified methodological approach for the introduction of parameters into families is...
For over 200 years, practitioners have been developing parametric families of probability distributions for data analysis. More recently, an active...
The linear mixed model has become the main parametric tool for the analysis of continuous longitudinal data, as the authors discussed in their 2000 book.
Without putting too much emphasis on software, the book shows how the different approaches can be implemented within the SAS software package.
The authors received the American Statistical Association's Excellence in Continuing Education Award based on short courses on longitudinal and incomplete data at the Joint Statistical Meetings of 2002 and 2004.
The linear mixed model has become the main parametric tool for the analysis of continuous longitudinal data, as the authors discussed in their 2000...
Modern apparatuses allow us to collect samples of functional data, mainly curves but also images. On the other hand, nonparametric statistics produces useful tools for standard data exploration. This book links these two fields of modern statistics by explaining how functional data can be studied through parameter-free statistical ideas. This book starts from theoretical foundations including functional nonparametric modeling, description of the mathematical framework, construction of the statistical methods, and statements of their asymptotic behaviors. It proceeds to computational issues...
Modern apparatuses allow us to collect samples of functional data, mainly curves but also images. On the other hand, nonparametric statistics produ...
Missing data arise in almost all scientific disciplines. In many cases, the treatment of missing data in an analysis is carried out in a casual and ad-hoc manner, leading, in many cases, to invalid inference and erroneous conclusions. In the past 20 years or so, there has been a serious attempt to understand the underlying issues and difficulties that come about from missing data and their impact on subsequent analysis. There has been a great deal written on the theory developed for analyzing missing data for finite-dimensional parametric models. This includes an extensive literature on...
Missing data arise in almost all scientific disciplines. In many cases, the treatment of missing data in an analysis is carried out in a casual and...
Geostatistics is concerned with estimation and prediction problems for spatially continuous phenomena, using data obtained at a limited number of spatial locations. The name reflects its origins in mineral exploration, but the methods are now used in a wide range of settings including public health and the physical and environmental sciences. Model-based geostatistics refers to the application of general statistical principles of modeling and inference to geostatistical problems. This volume is the first book-length treatment of model-based geostatistics.
The authors have written an...
Geostatistics is concerned with estimation and prediction problems for spatially continuous phenomena, using data obtained at a limited number of s...
