This textbook provides a step-by-step introduction to the tools and principles of high-dimensional statistics. Each chapter is complemented by numerous exercises, many of them with detailed solutions, and computer labs in R that convey valuable practical insights. The book covers the theory and practice of high-dimensional linear regression, graphical models, and inference, ensuring readers have a smooth start in the field. It also offers suggestions for further reading. Given its scope, the textbook is intended for beginning graduate and advanced undergraduate students in statistics, biostatistics, and bioinformatics, though it will be equally useful to a broader audience.
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1 | (36) |
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1.1 Embracing High-Dimensionality |
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2 | (3) |
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1.2 Statistical Limitations of Classical Estimators |
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5 | (5) |
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1.3 Incorporating Prior Information |
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10 | (3) |
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1.4 Regularization for Increasing the Numerical Stability* |
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13 | (5) |
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18 | (1) |
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19 | (6) |
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1.7 R Lab: Least-Squares vs. Ridge Estimation |
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25 | (9) |
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34 | (3) |
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37 | (44) |
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38 | (3) |
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2.2 Sparsity-Inducing Prior Functions |
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41 | (4) |
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2.3 Post-Processing Methods |
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45 | (3) |
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48 | (5) |
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2.5 Optimality Conditions* |
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53 | (10) |
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63 | (8) |
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71 | (6) |
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77 | (4) |
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81 | (28) |
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82 | (3) |
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3.2 Gaussian Graphical Models |
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85 | (2) |
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3.3 Maximum Regularized Likelihood Estimation |
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87 | (4) |
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3.4 Neighborhood Selection |
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91 | (4) |
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95 | (3) |
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3.6 R Lab: Estimating a Gene-Gene Coactivation Network |
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98 | (9) |
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107 | (2) |
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4 Tuning-Parameter Calibration |
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109 | (30) |
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110 | (3) |
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4.2 Bounds on the Lasso's Effective Noise |
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113 | (3) |
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116 | (5) |
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121 | (6) |
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127 | (4) |
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4.6 R Lab: Cross-Validation |
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131 | (4) |
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135 | (4) |
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139 | (30) |
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140 | (6) |
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146 | (7) |
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153 | (4) |
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5.4 R Lab: Confidence Intervals in Low and High Dimensions |
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157 | (9) |
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166 | (3) |
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169 | (42) |
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170 | (5) |
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175 | (7) |
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6.3 Prediction Guarantees |
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182 | (10) |
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6.4 Prediction Guarantees for Sparse and Weakly Correlated Models |
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192 | (12) |
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204 | (4) |
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208 | (3) |
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7 Theory II: Estimation and Support Recovery |
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211 | (28) |
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212 | (1) |
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7.2 Estimation Guarantees in -loss |
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213 | (5) |
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7.3 Estimation Guarantees in -loss |
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218 | (13) |
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7.4 Support Recovery Guarantees |
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231 | (4) |
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235 | (2) |
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237 | (2) |
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Supplementary Information |
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239 | (99) |
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240 | (69) |
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A.1 Solutions for Chap. 1 |
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240 | (17) |
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A.2 Solutions for Chap. 2 |
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257 | (14) |
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A.3 Solutions for Chap. 3 |
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271 | (14) |
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A.4 Solutions for Chap. 4 |
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285 | (3) |
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A.5 Solutions for Chap. 5 |
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288 | (7) |
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A.6 Solutions for Chap. 6 |
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295 | (5) |
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A.7 Solutions for Chap. 7 |
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300 | (9) |
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B Mathematical Background |
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309 | (29) |
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309 | (3) |
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312 | (26) |
| Bibliography |
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338 | (7) |
| Index |
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345 | |
Johannes Lederer is a Professor of Statistics at the Ruhr-University Bochum, Germany. He received his PhD in mathematics from the ETH Zürich and subsequently held positions at UC Berkeley, Cornell University, and the University of Washington. He has taught high-dimensional statistics to applied and mathematical audiences alike, e.g. as a Visiting Professor at the Institute of Statistics, Biostatistics, and Actuarial Sciences at UC Louvain, and at the University of Hong Kong Business School.
Lisainfo e-raamatute kohta