We consider debiased inference on finite-dimensional functionals of infinite-dimensional least-squares solutions to inverse problems as a way to avoid having to assume exact solutions exist. Such assumptions are substantive and not innocuous, and their failure may imperil inference when we impose them on the statistical model. Our approach instead allows us to conduct inference on a quantity that is defined regardless of solutions existing and coincides with the usual estimands when they do. For the case of instrumental variables, this means we can motivate the analysis with structural models but these do not need to hold exactly for the semiparametric inferential procedure to remain valid.

翻译：我们考虑对逆问题无穷维最小二乘解的有限维泛函进行去偏推断，以避免假设精确解的存在。此类假设具有实质性且非无害，若将其强加于统计模型，其失效可能危及推断的有效性。我们的方法允许我们对无论解是否存在均有定义的量进行推断，且当解存在时该量与通常的估计量一致。就工具变量情形而言，这意味着分析虽可由结构模型驱动，但半参数推断程序的有效性并不要求这些模型精确成立。