The PIT-trap-A "model-free" bootstrap procedure for inference about regression models with discrete, multivariate...

Area of Science:

• Statistics
• Computational Statistics
• Econometrics

Background:

• Traditional bootstrap methods struggle with non-identically distributed residuals in regression models.
• Existing techniques are not suitable for logistic, Poisson, or generalized estimating equations.
• Handling clustered or multivariate data presents challenges for standard residual resampling.

Purpose of the Study:

• To propose a new bootstrap method, the PIT-trap, for regression settings with non-identically distributed residuals.
• To adapt model-free bootstrap concepts for discrete and multivariate data.
• To preserve the marginal distribution of data and correlations in multivariate settings.

Main Methods:

• The PIT-trap utilizes probability integral transform (PIT) residuals.
• It assumes data originates from a marginal distribution F of known parametric form.
• Bootstrapping rows of PIT-residuals preserves correlations without explicit modeling.

Main Results:

• The PIT-trap method preserves the marginal distribution of data.
• It enables second-order correctness for pivotal PIT-trap test statistics.
• The method demonstrated improved properties compared to competing resampling methods in simulations and ecological data.

Conclusions:

• The PIT-trap offers a robust solution for bootstrapping residuals in complex regression scenarios.
• It provides a "model-free bootstrap" alternative suitable for discrete and multivariate data.
• This novel approach enhances statistical inference by preserving crucial data properties.