  We present a new algorithm for boosting generalized additive models for
location, scale and shape (GAMLSS) that allows to incorporate stability
selection, an increasingly popular way to obtain stable sets of covariates
while controlling the per-family error rate (PFER). The model is fitted
repeatedly to subsampled data and variables with high selection frequencies are
extracted. To apply stability selection to boosted GAMLSS, we develop a new
"noncyclical" fitting algorithm that incorporates an additional selection step
of the best-fitting distribution parameter in each iteration. This new
algorithms has the additional advantage that optimizing the tuning parameters
of boosting is reduced from a multi-dimensional to a one-dimensional problem
with vastly decreased complexity. The performance of the novel algorithm is
evaluated in an extensive simulation study. We apply this new algorithm to a
study to estimate abundance of common eider in Massachusetts, USA, featuring
excess zeros, overdispersion, non-linearity and spatio-temporal structures.
Eider abundance is estimated via boosted GAMLSS, allowing both mean and
overdispersion to be regressed on covariates. Stability selection is used to
obtain a sparse set of stable predictors.
