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Teaching GuideTerm Faculty of Computer Science |
| Mestrado Universitario en Técnicas Estadísticas (Plan 2019) |
 Subjects |
| Resampling Techniques |
| Contents |
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| Identifying Data | 2022/23 | |||||||||||||
| Subject | Resampling Techniques | Code | 614493130 | |||||||||||
| Study programme |
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| Descriptors | Cycle | Period | Year | Type | Credits | |||||||||
| Official Master's Degree | 1st four-month period |
Second | Optional | 5 | ||||||||||
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| Topic | Sub-topic |
| 1. Motivation of the Bootstrap principle. | Uniform bootstrap. Bootstrap distribution calculation: exact distribution and Monte Carlo approximation. Examples. Tools available in R. Parallel computing. |
| 2. Application to the estimation of the precision and bias of an estimator. | Application of the Bootstrap to estimate the precision and the bias of an estimator. Examples. The Jackknife method. Motivation of the Jackknife method. Jackknife estimation of the precision and bias of an estimator. Bootstrap / Jackknife relationship in these estimation problems. Examples. Simulation studies. |
| 3. Variations of the uniform Bootstrap. | Parametric Bootstrap, symmetrized Bootstrap, smoothed Bootstrap, weighted Bootstrap and biased Bootstrap. Discussion and examples. Validity of the Bootstrap approach. Examples. |
| 4. Applications of Bootstrap to construct confidence intervals. | Percentile method, percentile-t method, symmetrized percentile-t method . Examples. Simulation studies. |
| 7. Bootstrap applications in hypothesis testing. | P-value approximation by resampling. Parametric bootstrap tests. Permutations tests. Semi-parametric bootstrap tests. |
| 5. Bootstrap and nonparametric density estimation. | Bootstrap approximation for the distribution of the Parzen-Rosenblatt estimator. The Bootstrap in the selection of the smoothing parameter. |
| 6. Bootstrap for regression function estimation. | The Bootstrap in Regression and Correlation. Bootstrap and nonparametric estimation of the regression function. Bootstrap approximation of the distribution of the Nadaraya-Watson estimator. Different resampling methods and results. |
| 8. Bootstrap for censored data. | Introduction to censored data. Bootstrap resampling plans in the presence of censorship. Relations among them. Implementation in R. |
| 9. Bootstrap with dependent data. | Introduction to the usual conditions of dependency and dependent data models. Parametric models of dependence. General dependence situations: Moving Block Bootstrap, Stationary Bootstrap and Subsampling method. Implementation in R. The bootstrap in Spatial Statistics. |
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