Abstract : The Usher model is a matrix model describing a size-structured population that is characterised by
a restriction on the transitions between the state classes. It is well adapted to describe the dynamic
of a forest stand and is used to deal with forest management. This study turns on predictions in
the stationary state of the model. The main object is the construction of confidence intervals of
these predictions. First, asymptotic confidence intervals are built by using the maximum likelihood
estimator of predictions. The asymptotic distribution of these estimators is obtained by the delta
method. These results are extend in an other chapter to the more general density-dependant Usher
model, where the parameters depend on the varying characteristics of the population during time.
The existence and the uniqueness of the stationary distribution vector are firstly verified. Second,
the asymptotic confidence intervals are refined by searching robust estimators of model parameters.
The construction of these estimators respects the model constraints concerning its discrete structure
and the dynamic of the population. The parameters estimates are L-estimators expressed in a
multidimensional statistical model. The robustness criteria used is the estimator's sensibility based
on the influence function. The theoretical results are applied on a real data set of a forest stand in
French Guyana and the practical implications are discussed.