# Elements of Computational Statistics

Springer Science & Business Media, Apr 18, 2006 - Computers - 420 pages
In recent years developments in statistics have to a great extent gone hand in hand with developments in computing. Indeed, many of the recent advances in statistics have been dependent on advances in computer science and techn- ogy. Many of the currently interesting statistical methods are computationally intensive, eitherbecausetheyrequireverylargenumbersofnumericalcompu- tions or because they depend on visualization of many projections of the data. The class of statistical methods characterized by computational intensity and the supporting theory for such methods constitute a discipline called “com- tational statistics”. (Here, I am following Wegman, 1988, and distinguishing “computationalstatistics”from“statisticalcomputing”, whichwetaketomean “computational methods, including numerical analysis, for statisticians”.) The computationally-intensive methods of modern statistics rely heavily on the developments in statistical computing and numerical analysis generally. Computational statistics shares two hallmarks with other “computational” sciences, such as computational physics, computational biology, and so on. One is a characteristic of the methodology: it is computationally intensive. The other is the nature of the tools of discovery. Tools of the scienti?c method have generally been logical deduction (theory) and observation (experimentation). The computer, used to explore large numbers of scenarios, constitutes a new type of tool. Use of the computer to simulate alternatives and to present the research worker with information about these alternatives is a characteristic of thecomputationalsciences. Insomewaysthisusageisakintoexperimentation. The observations, however, are generated from an assumed model, and those simulated data are used to evaluate and study the model.

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### Contents

 Monte Carlo Methods for Inference 37 Randomization and Data Partitioning 67 4 83 Tools for Identification of Structure in Data 97 Estimation of Functions 125 Graphical Methods in Computational Statistics 149 Estimation of Probability Density Functions Using Parametric 193 Exercises 199
 Structure in Data 225 Statistical Models of Dependencies 291 Appendices 328 329 B Software for Random Number Generation 347 Notation and Definitions 359 Bibliography 375 Author Index 409 Subject Index 415

 Nonparametric Estimation of Probability Density Functions 201