This paper's main objective is to clearly describe the construction of a universal code for minimizing Davisson's minimax redundancy in a range where the true model and stochastic parameters are unknown. Minimax redundancy is defined as the maximum difference between the expected persymbol code length and the per-symbol source entropy in the source range. A universal coding scheme is here formulated in terms of the weight function, i.e., a method is presented for determining a weight function which minimizes the minimax redundancy even when the true model is unknown. It is subsequently shown that the minimax redundancy achieved through the presented coding method is upper-bounded by the minimax redundancy of Rissanen's semi-predictive coding method.