Random Projection Estimation of Discrete-Choice Models with Large Choice Sets
将机器学习的随机投影降维工具引入高维选择集的离散选择模型估计，利用循环单调性矩不等式进行半参数估计，无需对随机效用误差做分布假设，模拟和超市扫描数据应用表现良好。
We introduce random projection, an important dimension-reduction tool from machine learning, for the estimation of aggregate discrete-choice models with high-dimensional choice sets. Initially, high-dimensional data are projected into a lower-dimensional Euclidean space using random projections. Subsequently, estimation proceeds using cyclical monotonicity moment inequalities implied by the multinomial choice model; the estimation procedure is semiparametric and does not require explicit distributional assumptions to be made regarding the random utility errors. Our procedure is justified via the Johnson–Lindenstrauss lemma—the pairwise distances between data points are preserved through random projections. The estimator works well in simulations and in an application to a supermarket scanner data set. This paper was accepted by Juanjuan Zhang, marketing.