3. Chapter 4: Resampling Methods
This chapter covers resampling methods—computational techniques that use the data itself to quantify uncertainty, estimate sampling distributions, and validate models. Resampling methods are fundamental tools in modern data science because they make minimal parametric assumptions and work effectively even when theoretical distributions are unknown or intractable.
We explore two major families of resampling techniques: the bootstrap (sampling with replacement to estimate sampling distributions) and cross-validation (systematic data partitioning to assess predictive performance). These methods transform the classical problem of statistical inference—where we have one sample and want to understand what would happen with many samples—into a computational problem we can solve through simulation.
The chapter begins with the jackknife (a precursor to the bootstrap), then develops nonparametric and parametric bootstrap methods for constructing confidence intervals and correcting bias. We then turn to cross-validation techniques (leave-one-out and k-fold) for model selection and predictive evaluation, showing how resampling provides honest assessments of model performance.
Learning Objectives: Upon completion of this chapter, students will be able to:
Understand the jackknife as a resampling method for bias estimation and variance approximation
Implement and apply the nonparametric bootstrap for constructing sampling distributions
Distinguish between parametric and nonparametric bootstrap and choose appropriately
Construct bootstrap confidence intervals using percentile, BCa, and other methods
Apply bootstrap methods for bias correction of estimators
Understand when bootstrap methods fail (e.g., extreme order statistics, heavy-tailed distributions)
Implement leave-one-out cross-validation (LOOCV) for model assessment
Apply k-fold cross-validation and understand bias-variance tradeoffs in fold choice
Use cross-validation for model selection and hyperparameter tuning
Diagnose overfitting and assess predictive performance using resampling
Implement computational optimizations for resampling (parallel processing, efficient algorithms)