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Efficient budget plans are increasingly becoming important in mature developed countries, and the market mix model (MMM) plays an important role. We propose a new MMM methodology using a nonparametric approach that can be applied to a nonconvex shape frontier. The Free Disposal Hull (FDH) is known to be applicable to a nonconvex frontier, but the FDH frontier surface is stairlike stepwise. Thus, when we assume a monotonically increasing output with respect to increases in the input, the stepwise surface is inadequate for a sales response function for advertisement. The smoothing technique of the FDH frontier that we propose improves the performance in terms of budget optimization.
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