  The approximation of fixed-interval smoothing distributions is a key issue in
inference for general state-space hidden Markov models (HMM). This contribution
establishes non-asymptotic bounds for the Forward Filtering Backward Smoothing
(FFBS) and the Forward Filtering Backward Simulation (FFBSi) estimators of
fixed-interval smoothing functionals. We show that the rate of convergence of
the Lq-mean errors of both methods depends on the number of observations T and
the number of particles N only through the ratio T/N for additive functionals.
In the case of the FFBS, this improves recent results providing bounds
depending on T and the square root of N.
