∗ for the theory to work we need a compact support of ui. Issues arise when the estimator is near the boundary of the support - consistency is no longer assured. Li, Perrigne and Vong (2002, p 180 on) sort this out
∗ while nonparametric estimation is very attractive ex ante it may be that the data set you are facing works better with the extra structure imposed by a parametric specification. That is more structure may give you more power. In considering whether to go parametric think about what you want to use the estimates for, where identification is coming from and whether any auxiliary data can but used to justify the parametric assumption.
∗ there is still a lot of structure being imposed on the data here, particularly in stages (b) and (c). Take some time to think about how much work the functional form assumptions are doing in these stages.
∗ lastly, and most importantly, note the big assumptions on auction heterogeneity, bidder heterogeneity etc. More on this later...