| Description |
1 online resource (442 p.) |
| Series |
Springer Series in the Data Sciences |
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Springer series in the data sciences.
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| Contents |
Intro -- Preface -- Acknowledgments -- Contents -- List of Acronyms -- List of Nomenclatures -- List of Figures -- List of Tables -- I. Introduction to Big Data -- 1. Examples of Big Data -- 1.1. Multivariate Data -- 1.2. Categorical Data -- 1.3. Environmental Data -- 1.4. Genetic Data -- 1.5. Time Series Data -- 1.6. Ranking Data -- 1.7. Social Network Data -- 1.8. Symbolic Data -- 1.9. Image Data -- II. Statistical Inference for Big Data -- 2. Basic Concepts in Probability -- 2.1. Pearson System of Distributions -- 2.2. Modes of Convergence -- 2.3. Multivariate Central Limit Theorem |
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2.4. Markov Chains -- 3. Basic Concepts in Statistics -- 3.1. Parametric Estimation -- 3.2. Hypothesis Testing -- 3.3. Classical Bayesian Statistics -- 4. Multivariate Methods -- 4.1. Matrix Algebra -- 4.2. Multivariate Analysis as a Generalization of Univariate Analysis -- 4.2.1. The General Linear Model -- 4.2.2. One Sample Problem -- 4.2.3. Two-Sample Problem -- 4.3. Structure in Multivariate Data Analysis -- 4.3.1. Principal Component Analysis -- 4.3.2. Factor Analysis -- 4.3.3. Canonical Correlation -- 4.3.4. Linear Discriminant Analysis -- 4.3.5. Multidimensional Scaling |
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4.3.6. Copula Methods -- 5. Nonparametric Statistics -- 5.1. Goodness-of-Fit Tests -- 5.2. Linear Rank Statistics -- 5.3. U Statistics -- 5.4. Hoeffding's Combinatorial Central Limit Theorem -- 5.5. Nonparametric Tests -- 5.5.1. One-Sample Tests of Location -- 5.5.2. Confidence Interval for the Median -- 5.5.3. Wilcoxon Signed Rank Test -- 5.6. Multi-Sample Tests -- 5.6.1. Two-Sample Tests for Location -- 5.6.2. Multi-Sample Test for Location -- 5.6.3. Tests for Dispersion -- 5.7. Compatibility -- 5.8. Tests for Ordered Alternatives -- 5.9. A Unified Theory of Hypothesis Testing |
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5.9.1. Umbrella Alternatives -- 5.9.2. Tests for Trend in Proportions -- 5.10. Randomized Block Designs -- 5.11. Density Estimation -- 5.11.1. Univariate Kernel Density Estimation -- 5.11.2. The Rank Transform -- 5.11.3. Multivariate Kernel Density Estimation -- 5.12. Spatial Data Analysis -- 5.12.1. Spatial Prediction -- 5.12.2. Point Poisson Kriging of Areal Data -- 5.13. Efficiency -- 5.13.1. Pitman Efficiency -- 5.13.2. Application of Le Cam's Lemmas -- 5.14. Permutation Methods -- 6. Exponential Tilting and Its Applications -- 6.1. Neyman Smooth Tests |
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6.2. Smooth Models for Discrete Distributions -- 6.3. Rejection Sampling -- 6.4. Tweedie's Formula: Univariate Case -- 6.5. Tweedie's Formula: Multivariate Case -- 6.6. The Saddlepoint Approximation and Notions of Information -- 7. Counting Data Analysis -- 7.1. Inference for Generalized Linear Models -- 7.2. Inference for Contingency Tables -- 7.3. Two-Way Ordered Classifications -- 7.4. Survival Analysis -- 7.4.1. Kaplan-Meier Estimator -- 7.4.2. Modeling Survival Data -- 8. Time Series Methods -- 8.1. Classical Methods of Analysis -- 8.2. State Space Modeling -- 9. Estimating Equations |
| Summary |
This book presents a variety of advanced statistical methods at a level suitable for advanced undergraduate and graduate students as well as for others interested in familiarizing themselves with these important subjects. It proceeds to illustrate these methods in the context of real-life applications in a variety of areas such as genetics, medicine, and environmental problems. The book begins in Part I by outlining various data types and by indicating how these are normally represented graphically and subsequently analyzed. In Part II, the basic tools in probability and statistics are introduced with special reference to symbolic data analysis. The most useful and relevant results pertinent to this book are retained. In Part III, the focus is on the tools of machine learning whereas in Part IV the computational aspects of BIG DATA are presented. This book would serve as a handy desk reference for statistical methods at the undergraduate and graduate level as well as be useful in courses which aim to provide an overview of modern statistics and its applications |
| Notes |
9.1. Composite Likelihood |
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Includes index |
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Online resource; title from PDF title page (SpringerLink, viewed December 13, 2022) |
| Subject |
Big data.
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Mathematical statistics.
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Machine learning.
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Datos masivos
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Estadística matemática
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Aprendizaje automático (Inteligencia artificial)
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Big data
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Machine learning
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Mathematical statistics
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| Form |
Electronic book
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| ISBN |
9783031067846 |
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3031067843 |
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