RECIPROCAL PROCESSES ON A TREE-MODELING AND ESTIMATION ISSUES

Motivated by multiresolution decomposition methods such as the discret e wavelet transformation, me introduce reciprocal processes on truncat ed N-ary trees. We discuss the relationship between such processes and nearest neighbor models. We show that we can derive a recursive descr iption of the process, and that all reciprocal processes on N-ary tree s reduce to autoregressive processes in the case of zero-valued bounda ry values at the bottom of the tree, corresponding to truncation of th e tree. We then study the smoothing equations associated with such mod els.