  Model misspecification is ubiquitous in data analysis because the
data-generating process is often complex and mathematically intractable.
Therefore, assessing estimation uncertainty and conducting statistical
inference under a possibly misspecified working model is unavoidable. In such a
case, classical methods such as bootstrap and asymptotic theory-based inference
frequently fail since they rely heavily on the model assumptions. In this
article, we provide a new bootstrap procedure, termed local residual bootstrap,
to assess estimation uncertainty under model misspecification for generalized
linear models. By resampling the residuals from the neighboring observations,
we can approximate the sampling distribution of the statistic of interest
accurately. Instead of relying on the score equations, the proposed method
directly recreates the response variables so that we can easily conduct
standard error estimation, confidence interval construction, hypothesis
testing, and model evaluation and selection. It performs similarly to classical
bootstrap when the model is correctly specified and provides a more accurate
assessment of uncertainty under model misspecification, offering data analysts
an easy way to guard against the impact of misspecified models. We establish
desirable theoretical properties, such as the bootstrap validity, for the
proposed method using the surrogate residuals. Numerical results and real data
analysis further demonstrate the superiority of the proposed method.
