In spite of widespread use of generalized additive models (GAMs) to rem-
edy the “curse of dimensionality”, there is no well-grounded methodology developed
for simultaneous inference and variable selection for GAM in existing literature.
However, both are essential in enhancing the capability of statistical models. To this
end, we establish simultaneous confidence corridors (SCCs) and a type of Bayesian
information criterion (BIC) through the spline-backfitted kernel smoothing techniques
proposed in recent articles. To characterize the global features of each non-parametric
components, SCCs are constructed for testing their overall trends and entire shapes.
By extending the BIC in additive models with identity/trivial link, an asymptotically
consistent BIC approach for variable selection is built up in GAM to improve the par-
simony of model without loss of prediction accuracy. Simulations and a real example
corroborate the above findings.

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• Statistical inference for generalized additive models: simultaneous confidence corridors and variable selection