| Preface | p. VII |
| List of Abbreviations and Symbols | p. XVII |
| List of Figures | p. XIX |
| Statistical Background for Nonparametric Statistics and Functional Data | |
| Introduction to Functional Nonparametric Statistics | p. 5 |
| What is a Functional Variable? | p. 5 |
| What are Functional Datasets? | p. 6 |
| What are Nonparametric Statistics for Functional Data | p. 7 |
| Some Notation | p. 9 |
| Scope of the Book | p. 10 |
| Some Functional Datasets and Associated Statistical Problematics | p. 11 |
| Functional Chemometric Data | p. 11 |
| Description of Spectrometric Data | p. 12 |
| First Study and Statistical Problems | p. 13 |
| Speech Recognition Data | p. 15 |
| What are Speech Recognition Data? | p. 15 |
| First Study and Problematics | p. 15 |
| Electricity Consumption Data | p. 17 |
| The Data | p. 17 |
| The Forecasting Problematic | p. 18 |
| What is a Well-Adapted Space for Functional Data? | p. 21 |
| Closeness Notions | p. 21 |
| Semi-Metrics as Explanatory Tool | p. 22 |
| What about the Curse of Dimensionality? | p. 25 |
| Semi-Metrics in Practice | p. 28 |
| Functional PCA: a Tool to Build Semi-Metrics | p. 28 |
| PLS: a New Way to Build Semi-Metrics | p. 30 |
| Semi-metrics Based on Derivatives | p. 32 |
| R and S+ Implementations | p. 33 |
| What About Unbalanced Functional Data? | p. 33 |
| Semi-Metric Space: a Well-Adapted Framework | p. 35 |
| Local Weighting of Functional Variables | p. 37 |
| Why Use Kernel Methods for Functional Data? | p. 37 |
| Real Case | p. 38 |
| Multivariate Case | p. 39 |
| Functional Case | p. 41 |
| Local Weighting and Small Ball Probabilities | p. 42 |
| A Few Basic Theoretical Advances | p. 43 |
| Nonparametric Prediction from Functional Data | |
| Functional Nonparametric Prediction Methodologies | p. 49 |
| Introduction | p. 49 |
| Various Approaches to the Prediction Problem | p. 50 |
| Functional Nonparametric Modelling for Prediction | p. 52 |
| Kernel Estimators | p. 55 |
| Some Selected Asymptotics | p. 61 |
| Introduction | p. 61 |
| Almost Complete Convergence | p. 62 |
| Regression Estimation | p. 62 |
| Conditional Median Estimation | p. 66 |
| Conditional Mode Estimation | p. 70 |
| Conditional Quantile Estimation | p. 76 |
| Complements | p. 76 |
| Rates of Convergence | p. 79 |
| Regression Estimation | p. 79 |
| Conditional Median Estimation | p. 80 |
| Conditional Mode Estimation | p. 87 |
| Conditional Quantile Estimation | p. 90 |
| Complements | p. 92 |
| Discussion, Bibliography and Open Problems | p. 93 |
| Bibliography | p. 93 |
| Going Back to Finite Dimensional Setting | p. 94 |
| Some Tracks for the Future | p. 95 |
| Computational Issues | p. 99 |
| Computing Estimators | p. 99 |
| Prediction via Regression | p. 100 |
| Prediction via Functional Conditional Quantiles | p. 103 |
| Prediction via Functional Conditional Mode | p. 104 |
| Predicting Fat Content From Spectrometric Curves | p. 105 |
| Chemometric Data and the Aim of the Problem | p. 105 |
| Functional Prediction in Action | p. 106 |
| Conclusion | p. 107 |
| Nonparametric Classification of Functional Data | |
| Functional Nonparametric Supervised Classification | p. 113 |
| Introduction and Problematic | p. 113 |
| Method | p. 114 |
| Computational Issues | p. 116 |
| kNN Estimator | p. 116 |
| Automatic Selection of the kNN Parameter | p. 117 |
| Implementation: R/S+ Routines | p. 118 |
| Functional Nonparametric Discrimination in Action | p. 119 |
| Speech Recognition Problem | p. 119 |
| Chemometric Data | p. 122 |
| Asymptotic Advances | p. 122 |
| Additional Bibliography and Comments | p. 123 |
| Functional Nonparametric Unsupervised Classification | p. 125 |
| Introduction and Problematic | p. 125 |
| Centrality Notions for Functional Variables | p. 127 |
| Mean | p. 127 |
| Median | p. 129 |
| Mode | p. 130 |
| Measuring Heterogeneity | p. 131 |
| A General Descending Hierarchical Method | p. 131 |
| How to Build a Partitioning Heterogeneity Index? | p. 132 |
| How to Build a Partition? | p. 132 |
| Classification Algorithm | p. 134 |
| Implementation: R/S+ Routines | p. 135 |
| Nonparametric Unsupervised Classification in Action | p. 135 |
| Theoretical Advances on the Functional Mode | p. 137 |
| Hypotheses on the Distribution | p. 138 |
| The Kernel Functional Mode Estimator | p. 140 |
| Construction of the Estimates | p. 140 |
| Density Pseudo-Estimator: a.co. Convergence | p. 141 |
| Mode Estimator: a.co. Convergence | p. 144 |
| Comments and Bibliography | p. 145 |
| Conclusions | p. 146 |
| Nonparametric Methods for Dependent Functional Data | |
| Mixing, Nonparametric and Functional Statistics | p. 153 |
| Mixing: a Short Introduction | p. 153 |
| The Finite-Dimensional Setting: a Short Overview | p. 154 |
| Mixing in Functional Context | p. 155 |
| Mixing and Nonparametric Functional Statistics | p. 156 |
| Some Selected Asymptotics | p. 159 |
| Introduction | p. 159 |
| Prediction with Kernel Regression Estimator | p. 160 |
| Introduction and Notation | p. 160 |
| Complete Convergence Properties | p. 161 |
| An Application to the Geometrically Mixing Case | p. 163 |
| An Application to the Arithmetically Mixing Case | p. 166 |
| Prediction with Functional Conditional Quantiles | p. 167 |
| Introduction and Notation | p. 167 |
| Complete Convergence Properties | p. 168 |
| Application to the Geometrically Mixing Case | p. 171 |
| Application to the Arithmetically Mixing Case | p. 175 |
| Prediction with Conditional Mode | p. 177 |
| Introduction and Notation | p. 177 |
| Complete Convergence Properties | p. 178 |
| Application to the Geometrically Mixing Case | p. 183 |
| Application to the Arithmetically Mixing Case | p. 184 |
| Complements on Conditional Distribution Estimation | p. 185 |
| Convergence Results | p. 185 |
| Rates of Convergence | p. 187 |
| Nonparametric Discrimination of Dependent Curves | p. 189 |
| Introduction and Notation | p. 189 |
| Complete Convergence Properties | p. 190 |
| Discussion | p. 192 |
| Bibliography | p. 192 |
| Back to Finite Dimensional Setting | p. 192 |
| Some Open Problems | p. 193 |
| Application to Continuous Time Processes Prediction | p. 195 |
| Time Series and Nonparametric Statistics | p. 195 |
| Functional Approach to Time Series Prediction | p. 197 |
| Computational Issues | p. 198 |
| Forecasting Electricity Consumption | p. 198 |
| Presentation of the Study | p. 198 |
| The Forecasted Electrical Consumption | p. 200 |
| Conclusions | p. 201 |
| Conclusions | |
| Small Ball Probabilities and Semi-metrics | p. 205 |
| Introduction | p. 205 |
| The Role of Small Ball Probabilities | p. 206 |
| Some Special Infinite Dimensional Processes | p. 207 |
| Fractal-type Processes | p. 207 |
| Exponential-type Processes | p. 209 |
| Links with Semi-metric Choice | p. 212 |
| Back to the One-dimensional Setting | p. 214 |
| Back to the Multi- (but Finite) -Dimensional Setting | p. 219 |
| The Semi-metric: a Crucial Parameter | p. 223 |
| Some Perspectives | p. 225 |
| Appendix: Some Probabilistic Tools | p. 227 |
| Almost Complete Convergence | p. 228 |
| Exponential Inequalities for Independent r.r.v. | p. 233 |
| Inequalities for Mixing r.r.v. | p. 235 |
| References | p. 239 |
| Index | p. 255 |
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