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Table of Contents
Intro; Preface; Contents; Part I Overview; 1 Statistics, Statisticians, and the Internet of Things; 1.1 Introduction; 1.1.1 The Internet of Things; 1.1.2 What Is Big Data in an Internet of Things?; 1.1.3 Building Blocks; 1.1.4 Ubiquity; 1.1.5 Consumer Applications; 1.1.6 The Internets of [Infrastructure] Things; 1.1.7 Industrial Scenarios; 1.2 What Kinds of Statistics Are Needed for Big IoT Data?; 1.2.1 Coping with Complexity; 1.2.2 Privacy; 1.2.3 Traditional Statistics Versus the IoT; 1.2.4 A View of the Future of Statistics in an IoT World; 1.3 Big Data in the Real World; 1.3.1 Skills
1.3.2 Politics1.3.3 Technique; 1.3.4 Traditional Databases; 1.3.5 Cognition; 1.4 Conclusion; 2 Cognitive Data Analysis for Big Data; 2.1 Introduction; 2.1.1 Big Data; 2.1.2 Defining Cognitive Data Analysis; 2.1.3 Stages of CDA; 2.2 Data Preparation; 2.2.1 Natural Language Query; 2.2.2 Data Integration; 2.2.3 Metadata Discovery; 2.2.4 Data Quality Verification; 2.2.5 Data Type Detection; 2.2.6 Data Lineage; 2.3 Automated Modeling; 2.3.1 Descriptive Analytics; 2.3.2 Predictive Analytics; 2.3.3 Starting Points; 2.3.4 System Recommendations; 2.4 Application of Results; 2.4.1 Gaining Insights
2.4.2 Sharing and Collaborating2.4.3 Deployment; 2.5 Use Case; 2.6 Conclusion; References; Part II Methodology; 3 Statistical Leveraging Methods in Big Data; 3.1 Background; 3.2 Leveraging Approximation for Least Squares Estimator; 3.2.1 Leveraging for Least Squares Approximation; 3.2.2 A Matrix Approximation Perspective; 3.2.3 The Computation of Leveraging Scores; 3.2.4 An Innovative Proposal: Predictor-Length Method; 3.2.5 More on Modeling; 3.2.6 Statistical Leveraging Algorithms in the Literature: A Summary; 3.3 Statistical Properties of Leveraging Estimator
3.3.1 Weighted Leveraging Estimator3.3.2 Unweighted Leveraging Estimator; 3.4 Simulation Study; 3.4.1 UNIF and BLEV; 3.4.2 BLEV and LEVUNW; 3.4.3 BLEV and SLEV; 3.4.4 BLEV and PL; 3.4.5 SLEV and PL; 3.5 Real Data Analysis; 3.6 Beyond Linear Regression; 3.6.1 Logistic Regression; 3.6.2 Time Series Analysis; 3.7 Discussion and Conclusion; References; 4 Scattered Data and Aggregated Inference; 4.1 Introduction; 4.2 Problem Formulation; 4.2.1 Notations; 4.2.2 Review on M-Estimators; 4.2.3 Simple Averaging Estimator; 4.2.4 One-Step Estimator; 4.3 Main Results; 4.3.1 Assumptions
4.3.2 Asymptotic Properties and Mean Squared Errors (MSE) Bounds4.3.3 Under the Presence of Communication Failure; 4.4 Numerical Examples; 4.4.1 Logistic Regression; 4.4.2 Beta Distribution; 4.4.3 Beta Distribution with Possibility of Losing Information; 4.4.4 Gaussian Distribution with Unknown Mean and Variance; 4.5 Discussion on Distributed Statistical Inference; 4.6 Other Problems; 4.7 Conclusion; References; 5 Nonparametric Methods for Big Data Analytics; 5.1 Introduction; 5.2 Classical Methods for Nonparametric Regression; 5.2.1 Additive Models; 5.2.2 Generalized Additive Models (GAM)
1.3.2 Politics1.3.3 Technique; 1.3.4 Traditional Databases; 1.3.5 Cognition; 1.4 Conclusion; 2 Cognitive Data Analysis for Big Data; 2.1 Introduction; 2.1.1 Big Data; 2.1.2 Defining Cognitive Data Analysis; 2.1.3 Stages of CDA; 2.2 Data Preparation; 2.2.1 Natural Language Query; 2.2.2 Data Integration; 2.2.3 Metadata Discovery; 2.2.4 Data Quality Verification; 2.2.5 Data Type Detection; 2.2.6 Data Lineage; 2.3 Automated Modeling; 2.3.1 Descriptive Analytics; 2.3.2 Predictive Analytics; 2.3.3 Starting Points; 2.3.4 System Recommendations; 2.4 Application of Results; 2.4.1 Gaining Insights
2.4.2 Sharing and Collaborating2.4.3 Deployment; 2.5 Use Case; 2.6 Conclusion; References; Part II Methodology; 3 Statistical Leveraging Methods in Big Data; 3.1 Background; 3.2 Leveraging Approximation for Least Squares Estimator; 3.2.1 Leveraging for Least Squares Approximation; 3.2.2 A Matrix Approximation Perspective; 3.2.3 The Computation of Leveraging Scores; 3.2.4 An Innovative Proposal: Predictor-Length Method; 3.2.5 More on Modeling; 3.2.6 Statistical Leveraging Algorithms in the Literature: A Summary; 3.3 Statistical Properties of Leveraging Estimator
3.3.1 Weighted Leveraging Estimator3.3.2 Unweighted Leveraging Estimator; 3.4 Simulation Study; 3.4.1 UNIF and BLEV; 3.4.2 BLEV and LEVUNW; 3.4.3 BLEV and SLEV; 3.4.4 BLEV and PL; 3.4.5 SLEV and PL; 3.5 Real Data Analysis; 3.6 Beyond Linear Regression; 3.6.1 Logistic Regression; 3.6.2 Time Series Analysis; 3.7 Discussion and Conclusion; References; 4 Scattered Data and Aggregated Inference; 4.1 Introduction; 4.2 Problem Formulation; 4.2.1 Notations; 4.2.2 Review on M-Estimators; 4.2.3 Simple Averaging Estimator; 4.2.4 One-Step Estimator; 4.3 Main Results; 4.3.1 Assumptions
4.3.2 Asymptotic Properties and Mean Squared Errors (MSE) Bounds4.3.3 Under the Presence of Communication Failure; 4.4 Numerical Examples; 4.4.1 Logistic Regression; 4.4.2 Beta Distribution; 4.4.3 Beta Distribution with Possibility of Losing Information; 4.4.4 Gaussian Distribution with Unknown Mean and Variance; 4.5 Discussion on Distributed Statistical Inference; 4.6 Other Problems; 4.7 Conclusion; References; 5 Nonparametric Methods for Big Data Analytics; 5.1 Introduction; 5.2 Classical Methods for Nonparametric Regression; 5.2.1 Additive Models; 5.2.2 Generalized Additive Models (GAM)