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Ph. D. ThesisPh. D. Thesis 2. Theory – Fundamentals of the Multivariate Data Analysis 2. Theory – Fundamentals of the Multivariate Data Analysis 2.4. Data Splitting and Validation2.4. Data Splitting and Validation 2.4.3. Random Subsampling2.4.3. Random Subsampling
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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
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2.4.3.   Random Subsampling

Random sub­sampling, which is also known as Monte Carlo crossvalidation [19], as multiple holdout or as repeated evaluation set [20], is based on randomly splitting the data into subsets, whereby the size of the subsets is defined by the user [21]. The random partitioning of the data can be repeated arbitrarily often. In contrast to a full crossvalidation procedure, random subsampling has been shown to be asymptotically consistent [17] resulting in more pessimistic predictions of the test data compared with crossvalidation. The predictions of the test data give a realistic estimation of the predictions of external validation data [22].

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