High-dimensional statistical inference with general estimating equations are challenging and remain less explored. In this paper, we study two problems in the area: confidence set estimation for multiple components of the model parameters, and model specifications test. For the first one, we propose to construct a new set of estimating equations such that the impact from estimating the high-dimensional nuisance parameters becomes asymptotically negligible. The new construction enables us to estimate a valid confidence region by empirical likelihood ratio. For the second one, we propose a test statistic as the maximum of the marginal empirical likelihood ratios to quantify data evidence against the model specification. Our theory establishes the validity of the proposed empirical likelihood approaches, accommodating over-identification and exponentially growing data dimensionality. The numerical studies demonstrate promising performance and potential practical benefits of the new methods.

中文翻译：

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高维经验似然推断

具有一般估计方程的高维统计推断具有挑战性，并且很少被探索。在本文中，我们研究了该领域的两个问题：模型参数多分量的置信集估计和模型规范检验。对于第一个，我们建议构建一组新的估计方程，以便估计高维扰动参数的影响逐渐可以忽略不计。新结构使我们能够通过经验似然比估计有效的置信区域。对于第二个，我们提出了一个检验统计量作为边际经验似然比的最大值，以根据模型规范量化数据证据。我们的理论确立了所提议的经验似然方法的有效性，适应过度识别和指数增长的数据维度。数值研究证明了新方法的有希望的性能和潜在的实际好处。