Demand estimates are essential for addressing a wide range of positive and normative questions in economics that are known to depend on the shape—and notably the curvature—of the true demand functions. The existing frontier approaches, while allowing flexible substitution patterns, typically require the researcher to commit to a parametric specification. An open question is whether these a priori restrictions are likely to significantly affect the results. To address this, I develop a nonparametric approach to estimation of demand for differentiated products, which I then apply to California supermarket data. While the approach subsumes workhorse models such as mixed logit, it allows consumer behaviors and preferences beyond standard discrete choice, including continuous choices, complementarities across goods, and consumer inattention. When considering a tax on one good, the nonparametric approach predicts a much lower pass‐through than a standard mixed logit model. However, when assessing the market power of a multiproduct firm relative to that of a single‐product firm, the models give similar results. I also illustrate how the nonparametric approach may be used to guide the choice among parametric specifications.