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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