Nonparametric series regression often involves specification search over the tuning parameter, that is, evaluating estimates and confidence intervals with a different number of series terms. This paper develops pointwise and uniform inferences for conditional mean functions in nonparametric series estimations that are uniform in the number of series terms. As a result, this paper constructs confidence intervals and confidence bands with possibly data-dependent series terms that have valid asymptotic coverage probabilities. This paper also considers a partially linear model setup and develops inference methods for the parametric part uniform in the number of series terms. The finite sample performance of the proposed methods is investigated in various simulation setups as well as in an illustrative example, that is, the nonparametric estimation of the wage elasticity of the expected labor supply from Blomquist and Newey (2002, Econometrica 70, 2455–2480).

中文翻译：

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非参数系列估计中的推断与规范搜索系列项的数量

非参数级数回归通常涉及对调整参数的规范搜索，即使用不同数量的级数项评估估计值和置信区间。本文开发了非参数级数估计中条件均值函数的逐点和统一推理，这些估计在级数数上是统一的。因此，本文构建了具有有效渐近覆盖概率的可能与数据相关的序列项的置信区间和置信带。本文还考虑了部分线性模型设置，并开发了参数部分在系列项数上一致的推理方法。在各种模拟设置以及说明性示例中研究了所提出方法的有限样本性能，即计量经济学70, 2455–2480)。