| Biostatistics | p. 1 |
| Discriminant Analysis Based on Continuous and Discrete Variables | p. 3 |
| Introduction | p. 3 |
| Generalisation of the Mahalanobis Distance | p. 4 |
| Introduction | p. 4 |
| Kullback-Leibler Divergence | p. 5 |
| Asymptotic Distribution of Matusita Distance | p. 10 |
| Simulations | p. 12 |
| Methods and Stopping Rules for Selecting Variables | p. 13 |
| Reject Option | p. 15 |
| Distributional Result | p. 15 |
| Derivation of the Preliminary Test | p. 18 |
| Example | p. 22 |
| Location Model | p. 22 |
| Comparison with the Linear Discriminant Analysis | p. 24 |
| Conclusion | p. 24 |
| Bibliography | p. 25 |
| Longitudinal Data Analysis with Linear Regression | p. 29 |
| Introduction | p. 29 |
| Theoretical Aspects | p. 32 |
| The Fixed-effect Model | p. 32 |
| The Random Effects Model | p. 36 |
| Computing Fixed and Random-effect Models | p. 37 |
| Data Preparation | p. 37 |
| Fixed and Random-effect Linear Regression | p. 38 |
| Options for panfix | p. 38 |
| Options for panrand | p. 39 |
| Application | p. 40 |
| Results | p. 41 |
| Bibliography | p. 43 |
| A Kernel Method Used for the Analysis of Replicated Micro-array Experiments | p. 45 |
| Introduction | p. 45 |
| Statistical Model and Some Existing Methods | p. 46 |
| The Basic Model | p. 47 |
| The T-test | p. 47 |
| The Mixture Model Approach | p. 48 |
| A Fully Nonparametric Approach | p. 49 |
| Kernel Estimation of f[subscript 0] and f | p. 50 |
| The Reflection Approach in Kernel Estimation | p. 50 |
| Implementation of the Nonparametric Method | p. 51 |
| Data Analysis | p. 52 |
| Results Obtained with the Normal Mixture Model | p. 53 |
| Results Obtained with the Nonparametric Approach | p. 53 |
| A Simulation Study | p. 56 |
| Discussion and Concluding Remarks | p. 58 |
| Bibliography | p. 59 |
| Kernel Estimates of Hazard Functions for Biomedical Data Sets | p. 63 |
| Introduction | p. 63 |
| Kernel Estimate of the Hazard Function and Its Derivatives | p. 64 |
| Choosing the Shape of the Kernel | p. 68 |
| Choosing the Bandwidth | p. 69 |
| Description of the Procedure | p. 74 |
| Application | p. 75 |
| Bibliography | p. 83 |
| Partially Linear Models | p. 87 |
| Introduction | p. 87 |
| Estimation and Nonparametric Fits | p. 89 |
| Kernel Regression | p. 89 |
| Local Polynomial | p. 90 |
| Piecewise Polynomial | p. 93 |
| Least Square Spline | p. 96 |
| Heteroscedastic Cases | p. 97 |
| Variance Is a Function of Exogenous Variables | p. 98 |
| Variance Is an Unknown Function of T | p. 99 |
| Variance Is a Function of the Mean | p. 99 |
| Real Data Examples | p. 100 |
| Bibliography | p. 102 |
| Analysis of Contingency Tables | p. 105 |
| Introduction | p. 105 |
| Log-linear Models | p. 105 |
| Log-linear Models for Two-way Contingency Tables | p. 106 |
| Log-linear Models for Three-way Contingency Tables | p. 107 |
| Generalized Linear Models | p. 109 |
| Fitting to Log-linear Models | p. 111 |
| Inference for Log-linear Models Using XploRe | p. 113 |
| Estimation of the Parameter Vector [lambda] | p. 113 |
| Computing Statistics for the Log-linear Models | p. 113 |
| Model Comparison and Selection | p. 114 |
| Numerical Analysis of Contingency Tables | p. 115 |
| Testing Independence | p. 115 |
| Model Comparison | p. 119 |
| Bibliography | p. 124 |
| Identifying Coexpressed Genes | p. 125 |
| Introduction | p. 125 |
| Methodology and Implementation | p. 127 |
| Weighting Adjustment | p. 128 |
| Clustering | p. 132 |
| Concluding Remarks | p. 142 |
| Bibliography | p. 144 |
| Bootstrap Methods for Testing Interactions in GAMs | p. 147 |
| Introduction | p. 147 |
| Logistic GAM with Interactions | p. 149 |
| Estimation: the Local Scoring Algorithm | p. 150 |
| Bootstrap-based Testing for Interactions | p. 152 |
| Likelihood Ratio-based Test | p. 153 |
| Direct Test | p. 153 |
| Bootstrap Approximation | p. 153 |
| Simulation Study | p. 154 |
| Application to Real Data Sets | p. 156 |
| Neural Basis of Decision Making | p. 156 |
| Risk of Post-operative Infection | p. 159 |
| Discussion | p. 162 |
| Appendix | p. 163 |
| Bibliography | p. 165 |
| Survival Trees | p. 167 |
| Introduction | p. 167 |
| Methodology | p. 170 |
| Splitting Criteria | p. 170 |
| Pruning | p. 173 |
| The Quantlet stree | p. 174 |
| Syntax | p. 174 |
| Example | p. 175 |
| Bibliography | p. 179 |
| A Semiparametric Reference Curves Estimation | p. 181 |
| Introduction | p. 181 |
| Kernel Estimation of Reference Curves | p. 184 |
| A Semiparametric Approach Via Sliced Inverse Regression | p. 187 |
| Dimension Reduction Context | p. 187 |
| Estimation Procedure | p. 191 |
| Asymptotic Property | p. 192 |
| A Simulated Example | p. 193 |
| Case Study on Biophysical Properties of the Skin | p. 195 |
| Overview of the Variables | p. 196 |
| Methodological Procedure | p. 197 |
| Results and Interpretation | p. 198 |
| Conclusion | p. 200 |
| Bibliography | p. 201 |
| Survival Analysis | p. 207 |
| Introduction | p. 207 |
| Data Sets | p. 208 |
| Data on the Period up to Sympton Recurrence | p. 208 |
| Kaplan-Meier Estimate | p. 208 |
| Log-rank Test | p. 210 |
| Data for Aseptic Necrosis | p. 211 |
| Kaplan-Meier Estimate | p. 214 |
| Log-rank Test | p. 214 |
| Cox's Regression | p. 215 |
| Bibliography | p. 217 |
| Related Sciences | p. 219 |
| Ozone Pollution Forecasting | p. 221 |
| Introduction | p. 221 |
| A Brief Analysis of the Data | p. 222 |
| Description of the Data | p. 222 |
| Principal Component Analysis | p. 224 |
| Functional Principal Component Analysis | p. 225 |
| Functional Linear Model | p. 226 |
| Spline Estimation of [alpha] | p. 227 |
| Selection of the Parameters | p. 228 |
| Multiple Functional Linear Model | p. 229 |
| Functional Linear Regression for Conditional Quantiles Estimation | p. 231 |
| Spline Estimator of [Psi][subscript alpha] | p. 232 |
| Multiple Conditional Quantiles | p. 234 |
| Application to Ozone Prediction | p. 235 |
| Prediction of the Conditional Mean | p. 236 |
| Prediction of the Conditional Median | p. 236 |
| Analysis of the Results | p. 238 |
| Bibliography | p. 242 |
| Nonparametric Functional Chemometric Analysis | |
| Introduction | p. 245 |
| General Considerations | p. 246 |
| Introduction to Spectrometric Data | p. 246 |
| Introduction to Nonparametric Statistics for Curves | p. 248 |
| Notion of Proximity Between Curves | p. 249 |
| XploRe Quantlets for Proximity Between Curves | p. 251 |
| Functional Nonparametric Regression | p. 252 |
| The Statistical Problem | p. 252 |
| The Nonparametric Functional Estimate | p. 253 |
| Prediction of Fat Percentage from Continuous Spectrum | p. 254 |
| The XploRe Quantlet | p. 255 |
| Comments on Bandwidth Choice | p. 256 |
| Nonparametric Curves Discrimination | p. 257 |
| The Statistical Problem | p. 257 |
| A Nonparametric Curves Discrimination Method | p. 258 |
| Discrimination of Spectrometric Curves | p. 260 |
| The XploRe Quantlet | p. 261 |
| Concluding Comments | p. 262 |
| Bibliography | p. 263 |
| Variable Selection in Principal Component Analysis | p. 265 |
| Introduction | p. 265 |
| Variable Selection in PCA | p. 267 |
| Modified PCA | p. 268 |
| Selection Procedures | p. 269 |
| Quantlet | p. 272 |
| Examples | p. 273 |
| Artificial Data | p. 273 |
| Application Data | p. 279 |
| Bibliography | p. 282 |
| Spatial Statistics | p. 285 |
| Introduction | p. 285 |
| Analysis of Geostatistical Data | p. 287 |
| Trend Surfaces | p. 288 |
| Kriging | p. 290 |
| Correlogram and Variogram | p. 292 |
| Spatial Point Process Analysis | p. 297 |
| Discussion | p. 303 |
| Acknowledgements | p. 303 |
| Bibliography | p. 303 |
| Functional Data Analysis | p. 305 |
| Introduction | p. 305 |
| Functional Basis Expansion | p. 307 |
| Fourier Basis | p. 308 |
| Polynomial Basis | p. 309 |
| B-Spline Basis | p. 309 |
| Data Set as Basis | p. 309 |
| Approximation and Coefficient Estimation | p. 310 |
| Software Implementation | p. 312 |
| Temperature Example | p. 313 |
| Functional Principal Components | p. 314 |
| Implementation | p. 317 |
| Data Set as Basis | p. 319 |
| Smoothed Principal Components Analysis | p. 321 |
| Implementation Using Basis Expansion | p. 323 |
| Temperature Example | p. 323 |
| Bibliography | p. 326 |
| Analysis of Failure Time with Microearthquakes Applications | p. 329 |
| Introduction | p. 329 |
| Kernel Estimation of Hazard Function | p. 330 |
| An Application to Real Data | p. 336 |
| The Occurrence Process of Earthquakes | p. 336 |
| Galicia Earthquakes Data | p. 337 |
| Conclusions | p. 342 |
| Bibliography | p. 343 |
| Landcover Prediction | p. 347 |
| Introduction | p. 347 |
| Presentation of the Data | p. 348 |
| The Area: the Garrotxes | p. 348 |
| The Data Set | p. 348 |
| The Multilogit Regression Model | p. 349 |
| Penalized Log-likelihood Estimation | p. 351 |
| Polychotomous Regression in Action | p. 352 |
| Results and Interpretation | p. 353 |
| Bibliography | p. 356 |
| The Application of Fuzzy Clustering to Satellite Images Data | p. 357 |
| Introduction | p. 357 |
| Remote Sensing | p. 358 |
| Fuzzy C-means Method | p. 359 |
| Data and Methods | p. 361 |
| Results and Discussions | p. 362 |
| Bibliography | p. 366 |
| Index | p. 367 |
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