Statisticians quantify uncertainty in inference from random data to parameters through the sampling distributions of statistical functionals. These distributions are inaccessible in all but the simplest and most implausible cases. The bootstrap principle: sampling distributions under a good estimate of the truth are close to the true sampling distributions. Parametric bootstrapping: methods for finding standard errors, biases and confidence intervals, and for performing hypothesis tests. Double-bootstraps. Examples of parametric distribution with Pareto's law of income inequality. Non-parametric bootstrapping: using the empirical distribution itself as our model. The Pareto distribution continued. Bootstrapping regressions: resampling data-points versus resampling residuals; resampling of residuals under heteroskedasticity. Examples with homework data. Cautions on bootstrapping with dependent data. When does the bootstrap fail?
Posted at February 04, 2011 01:37 | permanent link