viii Contents Exercises 191 Chapter 14. Dimension and Structure in Nonparametric Regression 193 §14.1. Multiple Regression Model 193 §14.2. Additive regression 196 §14.3. Single-Index Model 199 §14.4. Proofs of Technical Results 206 Exercises 209 Chapter 15. Adaptive Estimation 211 §15.1. Adaptive Rate at a Point. Lower Bound 211 §15.2. Adaptive Estimator in the Sup-Norm 215 §15.3. Adaptation in the Sequence Space 218 §15.4. Proofs of Lemmas 223 Exercises 225 Chapter 16. Testing of Nonparametric Hypotheses 227 §16.1. Basic Definitions 227 §16.2. Separation Rate in the Sup-Norm 229 §16.3. Sequence Space. Separation Rate in the L2-Norm 231 Exercises 237 Bibliography 239 Index of Notation 241 Index 243
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