Introduction to statistics : the nonparametric way
著者
書誌事項
Introduction to statistics : the nonparametric way
（Springer texts in statistics）
Springer-Verlag, c1991
- : us
- : gw
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注記
Includes index
内容説明・目次
- 巻冊次
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: us ISBN 9780387402727
内容説明
Taken literally, the title "All of Statistics" is an exaggeration. But in spirit, the title is apt, as the book does cover a much broader range of topics than a typical introductory book on mathematical statistics. This book is for people who want to learn probability and statistics quickly. It is suitable for graduate or advanced undergraduate students in computer science, mathematics, statistics, and related disciplines.
The book includes modern topics like non-parametric curve estimation, bootstrapping, and classification, topics that are usually relegated to follow-up courses. The reader is presumed to know calculus and a little linear algebra. No previous knowledge of probability and statistics is required. Statistics, data mining, and machine learning are all concerned with collecting and analysing data.
目次
Probability.- Random Variables.- Expectation.- Inequalities.- Convergence of Random Variables.- Models, Statistical Inference and Learning.- Estimating the CDF and Statistical Functionals.- The Bootstrap.- Parametric Inference.- Hypothesis Testing and p-values.- Bayesian Inference.- Statistical Decision Theory.- Linear and Logistic Regression.- Multivariate Models.- Inference about Independence.- Causal Inference.- Directed Graphs and Conditional Independence.- Undirected Graphs.- Loglinear Models.- Nonparametric Curve Estimation.- Smoothing Using Orthogonal Functions.- Classification.- Probability Redux: Stochastic Processes.- Simulation Methods.
- 巻冊次
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: gw ISBN 9783540972846
内容説明
The text introduces the student to the basic ideas of estimation and hypothesis testing early in the course after a rather brief introduction to data organization and some simple ideas about probability. Estimation and hypothesis testing are discussed in terms of the two-sample problem. The book exploits nonparametric ideas that rely on nothing more complicated than sample differences Y-X, referred to as elementary estimates, to define the Wilcoxon-Mann-Whitney test statistics and the related point and interval estimates. The ideas behind elementary estimates are then applied to the one-sample problem and to linear regression and rank correlation. Discussion of the Kruskal-Wallis and Friedman procedures for the k-sample problem rounds out the nonparametric coverage. The concluding chapters provide a discussion of Chi-square tests for the analysis of categorical data and introduce the student to the analysis of binomial data including the computation of power and sample size. Most chapters in the book have an appendix discussing relevant Minitab commands.
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