The Bootstrap Percentile confidence interval principle.

<p>Schematic of the bootstrap process. We want to estimate a confidence interval for the phase <i>θ</i>(<i>χ</i>). <i>R</i> training sets, <i>χ</i>¹*, …, <i>χ</i>^<i>R</i>* each of size <i>n</i> are generated using an appropriate resampling mechanism. The quantity of interest <i>θ</i>(<i>χ</i>) is computed from each bootstrap training set, and the values </p><p></p><p></p><p><mi>θ</mi><mo stretchy="false">(</mo></p><p><mo>χ</mo><mn>1</mn><mo>*</mo></p><mo stretchy="false">)</mo><mo>,</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>,</mo><mi>θ</mi><mo stretchy="false">(</mo><p><mo>χ</mo><mi>R</mi><mo>*</mo></p><mo stretchy="false">)</mo><p></p><p></p><p></p> are used to construct a confidence interval for the quantity <i>θ</i>(<i>χ</i>).<p>