Before revision:  The mean integrated squared error for the density estimator of a random variable in \mathbb{R the  California Department of Transportation to explore whether their choice of awarding construction contracts using a first price auction is cost minimizing  .
After revision:  The mean integrated squared error for the density estimator of a random variable in \mathbb{R the null hypothesis that the population density satisfies a shape constraint. Afterward, we provide sufficient conditions for these results to hold using an arbitrary shape constraint. This generalization is used to explore whether the California Department of Transportation to explore whether their choice of awarding construction contracts using a first price auction is cost minimizing .