  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.
