Fisher-whitened score M -estimation for robust inference in the Weibull model

Maximum likelihood inference for the two-parameter Weibull model can be highly sensitive to a few influential observations because its score is unbounded. Robust Weibull procedures often use probability plots, quantile methods, or robust summaries; few directly modify likelihood scores while supporting point and interval inference. We address this gap with centered Fisher-whitened score M-estimators using Huber and Tukey bisquare transformations. Whitening standardizes and decorrelates the shape and scale scores, while model-based centering preserves Fisher consistency. Under regularity conditions, we establish consistency and asymptotic normality for a locally identified root, show that its influence function is bounded, and construct log-scale Wald intervals using an empirical sandwich estimator of the Godambe covariance. Simulations show improved shape estimation and interval coverage relative to maximum likelihood under mild to moderate contamination by a component with a larger scale and a heavier tail, especially for moderate and larger shape values, while retaining high efficiency under the uncontaminated model. Applications to wind speed measurements and carbon-fiber breaking stresses illustrate upper-tail diagnostics and reduced sensitivity to influential observations.