Studentized
The observed statistic and each first-level bootstrap statistic are divided by an estimated standard deviation. Estimating those standard deviations requires a second bootstrap level.
studentized = TRUE
DOC 03 / 06Route comparison
Two routes, selected by one argument
Keep the studentized double-bootstrap default or choose a faster non-studentized single bootstrap.
Comparison
Studentized and non-studentized choices
Non-studentized
The observed statistic is compared directly with first-level bootstrap statistics. No nested variance bootstrap is performed.
studentized = FALSE
| Feature | Studentized | Non-studentized |
|---|---|---|
| Bootstrap levels | Two | One |
B1 | First-level replications | Single-bootstrap replications |
B2 | Nested variance replications; if omitted, 100 is used with a message | Not required or used |
| Lag handling | The selected p is retained across the corresponding outer and inner calculations | The selected p is retained for the single bootstrap |
Normality
The single-bootstrap combination
For studentized = FALSE, the implementation first obtains single-bootstrap p-values for sample skewness and kurtosis, then applies the Šidák combination
\[p_N = 1 - \{1 - \min(p_S,p_K)\}^{2}.\]
The robust-skewness p-value is reported separately and is not part of this normality combination.
Choice
Computation and finite-sample behavior
The non-studentized procedure avoids the nested variance bootstrap and is therefore substantially less computationally demanding. In the paper's simulations it often has comparable power, but it can exhibit greater size distortion, particularly for symmetry tests.
Practical guidance: Treat simulation findings as qualitative guidance rather than a guarantee for a particular series.