  In many prediction problems, it is not uncommon that the number of variables
used to construct a forecast is of the same order of magnitude as the sample
size, if not larger. We then face the problem of constructing a prediction in
the presence of potentially large estimation error. Control of the estimation
error is either achieved by selecting variables or combining all the variables
in some special way. This paper considers greedy algorithms to solve this
problem. It is shown that the resulting estimators are consistent under weak
conditions. In particular, the derived rates of convergence are either minimax
or improve on the ones given in the literature allowing for dependence and
unbounded regressors. Some versions of the algorithms provide fast solution to
problems such as Lasso.
