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Table of Contents
Preface; Contents; Part I General High-Dimensional Theory and Methods; Regularization After Marginal Learning for Ultra-High Dimensional Regression Models; 1 Introduction; 2 Model Setup and Several Methods in Variable Selection; 2.1 Model Setup and Notations; 2.2 Regularization Techniques; 2.3 Sure Independence Screening; 3 Regularization After Marginal Learning; 3.1 Algorithm; 3.2 Connections to SIS and RAR; 3.3 From RAM-2 to RAM; 4 Asymptotic Analysis; 4.1 Sure Independence Screening Property; 4.2 Sign Consistency for RAM-2; 4.3 Sign Consistency for RAM; 5 Numerical Study
5.1 Tuning Parameter Selection5.2 Simulations; 6 Discussion; Appendix; References; Empirical Likelihood Test for High Dimensional Generalized Linear Models; 1 Introduction; 2 The Proposed Test; 3 The Partial Test with Nuisance Parameters; 4 Simulation Study; 5 Data Analysis; 6 Discussion; Appendix; References; Random Projections for Large-Scale Regression; 1 Introduction; 2 Theoretical Results; 3 Averaged Compressed Least Squares; 4 Discussion; Appendix; References; Testing in the Presence of Nuisance Parameters: Some Comments on Tests Post-Model-Selection and Random Critical Values
Bias-Reduced Moment Estimators of Population Spectral Distribution and Their Applications1 Introduction; 2 Moments of a PSD and Their Bias-Reduced Estimators; 3 Test Procedure; 4 Simulation; 4.1 Case of Testing for Order Two PSDs; 4.2 Case of Testing for Order Three PSDs; 5 Conclusions and Remarks; 6 Proofs; 6.1 Proof of Theorem 1; 6.2 Proof of Theorem 4; References; Part II Network Analysis and Big Data; Statistical Process Control Charts as a Tool for Analyzing Big Data; 1 Introduction; 2 Conventional SPC Charts; 3 Dynamic Statistical Screening; 4 Profiles/Images Monitoring
5 Concluding RemarksReferences; Fast Community Detection in Complex Networks with a K-Depths Classifier; 1 Introduction; 2 Preliminaries and Background; 3 Community Detection Using L1 Data Depth; 3.1 Properties of Spectral Clustering K-Depths Algorithm; 4 Simulations; 4.1 Network Clustering with Two Groups; 4.2 Network Clustering with Outliers; 5 Application to Flickr Communities; 6 Conclusion and Future Work; References; How Different Are Estimated Genetic Networks of Cancer Subtypes?; 1 Introduction; 2 Network Reconstruction Methods; 2.1 Weighted Gene Correlation Network Analysis
5.1 Tuning Parameter Selection5.2 Simulations; 6 Discussion; Appendix; References; Empirical Likelihood Test for High Dimensional Generalized Linear Models; 1 Introduction; 2 The Proposed Test; 3 The Partial Test with Nuisance Parameters; 4 Simulation Study; 5 Data Analysis; 6 Discussion; Appendix; References; Random Projections for Large-Scale Regression; 1 Introduction; 2 Theoretical Results; 3 Averaged Compressed Least Squares; 4 Discussion; Appendix; References; Testing in the Presence of Nuisance Parameters: Some Comments on Tests Post-Model-Selection and Random Critical Values
Bias-Reduced Moment Estimators of Population Spectral Distribution and Their Applications1 Introduction; 2 Moments of a PSD and Their Bias-Reduced Estimators; 3 Test Procedure; 4 Simulation; 4.1 Case of Testing for Order Two PSDs; 4.2 Case of Testing for Order Three PSDs; 5 Conclusions and Remarks; 6 Proofs; 6.1 Proof of Theorem 1; 6.2 Proof of Theorem 4; References; Part II Network Analysis and Big Data; Statistical Process Control Charts as a Tool for Analyzing Big Data; 1 Introduction; 2 Conventional SPC Charts; 3 Dynamic Statistical Screening; 4 Profiles/Images Monitoring
5 Concluding RemarksReferences; Fast Community Detection in Complex Networks with a K-Depths Classifier; 1 Introduction; 2 Preliminaries and Background; 3 Community Detection Using L1 Data Depth; 3.1 Properties of Spectral Clustering K-Depths Algorithm; 4 Simulations; 4.1 Network Clustering with Two Groups; 4.2 Network Clustering with Outliers; 5 Application to Flickr Communities; 6 Conclusion and Future Work; References; How Different Are Estimated Genetic Networks of Cancer Subtypes?; 1 Introduction; 2 Network Reconstruction Methods; 2.1 Weighted Gene Correlation Network Analysis