Ph. D. Thesis 2. Theory – Fundamentals of the Multivariate Data Analysis 2.4. Data Splitting and Validation 2.4.2. Bootstrapping
 Home News About Me Ph. D. Thesis Abstract Table of Contents 1. Introduction 2. Theory – Fundamentals of the Multivariate Data Analysis 2.1. Overview of the Multivariate Quantitative Data Analysis 2.2. Experimental Design 2.3. Data Preprocessing 2.4. Data Splitting and Validation 2.4.1. Crossvalidation 2.4.2. Bootstrapping 2.4.3. Random Subsampling 2.4.4. Kennard Stones 2.4.5. Kohonen Neural Networks 2.4.6. Conclusions 2.5. Calibration of Linear Relationships 2.6. Calibration of Nonlinear Relationships 2.7. Neural Networks – Universal Calibration Tools 2.8. Too Much Information Deteriorates Calibration 2.9. Measures of Error and Validation 3. Theory – Quantification of the Refrigerants R22 and R134a: Part I 4. Experiments, Setups and Data Sets 5. Results – Kinetic Measurements 6. Results – Multivariate Calibrations 7. Results – Genetic Algorithm Framework 8. Results – Growing Neural Network Framework 9. Results – All Data Sets 10. Results – Various Aspects of the Frameworks and Measurements 11. Summary and Outlook 12. References 13. Acknowledgements Publications Research Tutorials Downloads and Links Contact Search Site Map Print this Page

### 2.4.2.   Bootstrapping

Bootstrap resampling was originally developed to help analysts determine how much their results might have changed if another random sample had been used instead and how different the results might be when a model is applied to new data. Bootstrapping has also gained an increasing popularity in the field of resampling small data sets [18]. Bootstrapping is based on sampling with replacement to form a calibration set. For the most popular variant, the 0.632 bootstrap, n times a sample is selected from n samples for the calibration set whereby the same sample can be selected several times. Then, the samples, which were not picked, are used for the test set. The chance that a particular sample is not picked for the calibration set is:

 (4)

Consequently, the test set contains about 36.8% of the samples and the calibration set about 63.2% with some samples replicated in the calibration set. Bootstrapping is not affected by asymptotic inconsistency and might be the best way of estimating the error for very small data sets whereby the complete procedure can be repeated arbitrarily often [9].

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