High covariate dimensionality is increasingly occurrent in model estimation, and existing techniques to address this issue typically require sparsity or discrete heterogeneity of the unobservable parameter vector. However, neither restriction may be supported by economic theory in some empirical contexts, leading to severe bias and misleading inference. The clustering-based grouped parameter estimator (GPE) introduced in this paper drops both restrictions in favour of the natural one that the parameter support be compact. GPE exhibits robust large sample properties under standard conditions and accommodates both sparse and non-sparse parameters whose support can be bounded away from zero. Extensive Monte Carlo simulations demonstrate the excellent performance of GPE in terms of bias reduction and size control compared to competing estimators. An empirical application of GPE to estimating price and income elasticities of demand for gasoline highlights its practical utility.

翻译：高协变量维度在模型估计中日益普遍，现有处理该问题的技术通常要求未观测参数向量具有稀疏性或离散异质性。然而，在某些实证背景下经济理论可能不支持这两种限制，从而导致严重偏差和误导性推论。本文提出的基于聚类的分组参数估计量（GPE）摒弃了这两种限制，转而采用参数支撑集具有紧致性这一自然假设。GPE在标准条件下展现出稳健的大样本性质，并能同时处理参数支撑集有界远离零的稀疏与非稀疏参数。大量蒙特卡洛模拟表明，与竞争性估计量相比，GPE在降低偏差和控制检验规模方面表现优异。将GPE应用于汽油需求价格弹性和收入弹性的实证研究，凸显了其实际应用价值。