This thesis develops systematically a formalism for Forest Sampling within an infinite population and superpopulation framework. The summations over finite populations or subpopulations of trees are replaced by the integration of functions over domains of the plane. It provides a synthetic treatment for design-based, model-based and model-dependent inference, with special attention paid to the incorporation of auxiliary information provided by Geographical Information System or Remote Sensing in the context of double sampling schemes. The problem of boundary effects at the forest edge is treated in the context of simple and double sampling with random cluster size. The solutions derived in the design-based and model-based approaches are simpler and more general than the classical results resting upon analysis of variance. A new model-based estimate of variance is proposed which is more efficient, under the model, than the design-based variance estimate. The asymptotic properties of estimates like consistency and efficiency are thoroughly discussed. Solutions are derived for the optimization of double sampling schemes with arbitrary 2nd stage inclusion probabilities and linear cost functions. The local estimation of small areas is also considered, as well as some specific numerical aspects of linear models. A detailed case study summarizes, illustrates and compares the various estimations procedures and gives a first validation of the local estimation techniques. It is argued that the various estimation procedures will tend to yield comparable results at the global level, while they may differ, even considerably, at the local level, particularly with respect to error estimation.
