Latent variable models are widely used to account for unobserved determinants of economic behavior. Traditional nonparametric methods to estimate latent heterogeneity do not scale well into multidimensional settings. Distributional restrictions alleviate tractability concerns but may impart non-trivial misspecification bias. Motivated by these concerns, this paper introduces a quasi-Bayes approach to estimate a large class of multidimensional latent variable models. Our approach to quasi-Bayes is novel in that we center it around relating the characteristic function of observables to the distribution of unobservables. We propose a computationally attractive class of priors that are supported on Gaussian mixtures and derive contraction rates for a variety of latent variable models.

翻译：潜变量模型被广泛用于解释经济行为中未被观测到的决定因素。传统的非参数方法在估计潜在异质性时难以扩展到多维设定。分布约束虽然缓解了可处理性问题，但可能引入显著的误设偏差。基于这些问题，本文提出了一种准贝叶斯方法，用于估计一大类多维潜变量模型。我们的准贝叶斯方法具有新颖性，其核心在于将可观测变量的特征函数与不可观测变量的分布联系起来。我们提出了一类计算上具有吸引力的先验分布，该分布以高斯混合为支撑，并推导了多种潜变量模型的压缩率。