A popular approach to perform inference on a target parameter in the presence of nuisance parameters is to construct estimating equations that are orthogonal to the nuisance parameters, in the sense that their expected first derivative is zero. Such first-order orthogonalization allows the estimator of the nuisance parameters to converge at a slower-than-parametric rate. It may, however, not suffice when the nuisance parameters are very imprecisely estimated. Leading examples are models for panel and network data that feature fixed effects. In this paper, we show how, in the conditional-likelihood setting, estimating equations can be constructed that are orthogonal to any chosen order $q$, in that their leading $q$ expected derivatives are zero. This yields estimators of target parameters that are unaffected by the presence of nuisance parameters to order $q$. In an empirical illustration, we apply our method to a fixed-effect model of team production.

翻译：在存在伴随参数的情况下，对目标参数进行推断的一种常用方法是构造关于伴随参数正交的估计方程，即其期望一阶导数为零。这种一阶正交化允许伴随参数的估计量以低于参数收敛率的速度收敛。然而，当伴随参数估计非常不精确时，仅有一阶正交可能并不足够。面板数据和网络数据模型中包含固定效应的情形是其主要示例。本文展示了在条件似然设定下，如何构造关于任意选定阶数 $q$ 正交的估计方程，即使其前 $q$ 阶期望导数为零。这产生了目标参数的估计量，其至 $q$ 阶不受伴随参数存在的影响。在一项实证示例中，我们将该方法应用于团队生产的固定效应模型。