Uniform consistency in nonparametric mixture models
研究了非参数混合模型及混合回归模型中回归函数的一致一致性估计，在一般条件下构造了一致估计量，并发展了新的技术工具来处理回归函数任意相交等挑战。
We study uniform consistency in nonparametric mixture models as well as closely related mixture of regression (also known as mixed regression) models, where the regression functions are allowed to be nonparametric and the error distributions are assumed to be convolutions of a Gaussian density. We construct uniformly consistent estimators under general conditions while simultaneously highlighting several pain points in extending existing pointwise consistency results to uniform results. The resulting analysis turns out to be nontrivial, and several novel technical tools are developed along the way. In the case of mixed regression, we prove L1 convergence of the regression functions while allowing for the component regression functions to intersect arbitrarily often, which presents additional technical challenges. We also consider generalizations to general (i.e., nonconvolutional) nonparametric mixtures.