Inference in Non-Standard Econometric Problems

经济学中的实证问题是通过计量经济模型来研究的。这些模型包含未知参数，这些参数通常是经验应用中感兴趣的对象。例如，人们可能有兴趣了解平均消费倾向，或者增加税收对劳动力供给的边际效应，研究人员使用数据和计量经济学分析来估计这些参数。显然，人们希望使用数据分析方法，使人们能够尽可能多地了解这些未知参数。对于一个大的模型集，如何这样做是很容易理解的，至少大致是这样。对于一个性能良好的模型的许多观测值，不知道参数的问题实际上等同于观察单个高斯（钟形）观测值的“标准问题”，该观测值具有已知的扩散和对应于未知参数的平均值。然而，对于一个不可忽略的模型子集，只有一个近似等价于不同的“非标准”问题。这些未知的相关模式使得不可能完美地了解参数估计量的传播，这导致了一个非标准的近似等效问题，其中单个高斯向量观测的传播是未知的。该提案研究了此类非标准问题，并寻求开发学习未知参数的方法。近似有效方法的推导涉及到适当的分析结果的发展，即非标准问题中潜在推理质量的准确上界，以及确定近似有效过程的数值方法，即推理质量接近上界的方法。

Empirical questions in economics are studied via econometric models. These models contain unknown parameters, which are typically the object of interest in empirical applications. For instance, one might be interested in learning about the average propensity to consume, or the marginal effect of a tax increase on labor supply, and researchers use data and econometrics analysis to estimate that parameter. Clearly, one would like to use methods of data analysis that allow one to learn as much as possible about these unknown parameters. And for a large set of models, it is well understood how to do so, at least approximately. With many observations from a well-behaved model, the problem of not knowing the parameter is effectively equivalent to the "standard problem" of observing a single Gaussian (bell-shaped) observation with known spread and a mean that corresponds to the unknown parameter. For a non-negligible subset of models, however, there is only an approximate equivalence to a different, "non-standard" problem. These unknown correlation patterns make it impossible to perfectly learn about the spread of the parameter estimator, which leads to a non-standard approximately equivalent problem where the spread of the single Gaussian vector observation is unknown. The proposal studies such non-standard problems, and seeks to develop ways of learning about the unknown parameters. The derivation of nearly efficient methods involves the development of appropriate analytical results, such accurate upper bounds on the potential quality of inference in non-standard problems, as well as numerical methods that determine a nearly efficient procedure, that is one with an inference quality close to the upper bound.