دانلود کتاب آمار ریاضی – جلد اول

In this preface, we start with an overview of developments in statistics since the first (1977) edition, then give separate overviews of Volumes I and II of the second edition. In the last 40 some years statistics has changed enormously under the impact of several forces: (1) The generation of what were once unusual types of data such as images, trees (phylogenetic and other), and other types of combinatorial objects. (2) The generation of enormous amounts of data—terabytes (the equivalent of 1012 characters) for an astronomical survey over three years. (3) The possibility of implementing computations of a magnitude that would have once been unthinkable. The underlying sources of these changes have been the exponential change in computing speed (Moore’s “law”) and the development of devices (computer controlled) using novel instruments and scientific techniques (e.g., NMR tomography, gene sequencing). These techniques often have a strong intrinsic computational component. Tomographic data are the result of mathematically based processing. Sequencing is done by applying computational algorithms to raw gel electrophoresis data. As a consequence the emphasis of statistical theory has shifted away from small sample optimality results in a number of directions: (1) Methods for inference based on larger numbers of observations and minimal assumptions—asymptoticmethods in non- and semiparametric models, models with “infinite” number of parameters. (2) The construction of models for time series, temporal spatial series, and other complex data structures using sophisticated probability modeling but again relying for analytical results on asymptotic approximation. Multiparameter models are the rule. (3) The use of methods of inference involving simulation as a key element such as the bootstrap and Markov Chain Monte Carlo.