Nonparametric Inferences for Additive Models
加性模型的非参数推断AI 解读 ↓
← 返回论文列表与筛选
阅读说明
本页整理公开书目信息，不生成学术质量评分。AI 解读根据题名及所注明的摘要或原文片段生成，未完成全文核验，可能有误；具体假设、证明与结论请核对原文。摘要保留来源文本，未经模型改写。
DOI 首次登记不等于接收或发表日期。部分更正、评论等条目没有独立摘要；缺少可靠材料时保留待补状态。
引用量采用 OpenAlex 单条关联记录，不合计多个记录；关联记录可能包含正式发表版本，不等于此版本单独引用。缺失不视为零，引用指标不代表论文质量。
关注作者按书目中的完整姓名匹配，同名和姓名变体需人工辨别。相关论文先按共享细分方向和具体方法排列，再参考通用方法与发表日期。
分类依据与纠错
AI 根据所提供的论文材料归类：摘要讨论通用加性回归检验，没有明确的因果、面板、时间序列或金融应用依据。
反馈分类问题
正在核对关联版本…
代码、数据与补充材料
正在核对对应版本的资源…
关注这篇论文的作者
加性模型的非参数推断
- 研究问题
- 使用回代算法估计加性模型后，如何检验某个加性分量是否显著或具有指定参数形式，并建立可用的非参数检验理论？
- 方法与思路
- 作者将广义似然比检验扩展到回代估计的加性模型，并针对参数化加性模型提出偏差校正，以构造相应检验统计量。
- 材料陈述的贡献
- 摘要称，检验具有不依赖干扰参数的渐近缩放卡方分布及 Wilks 现象，并达到非参数检验的最优收敛速率。
- 阅读关注点
- 应核对平滑方法、误差分布与零假设的限制，卡方缩放及自由度的计算方式，以及偏差校正和速率最优性的具体条件。
- 阅读边界
- 仅据版本未注明的 OpenAlex 摘要；模拟与实例的具体结果未提供，不能据此判断有限样本优势或推断刊本变化。
原文摘要
Additive models with backfitting algorithms are popular multivariate nonparametric fitting techniques. However, the inferences of the models have not been very well developed, due partially to the complexity of the backfitting estimators. There are few tools available to answer some important and frequently asked questions, such as whether a specific additive component is significant or admits a certain parametric form. In an attempt to address these issues, we extend the generalized likelihood ratio (GLR) tests to additive models, using the backfitting estimator. We demonstrate that under the null models, the newly proposed GLR statistics follow asymptotically rescaled chi-squared distributions, with the scaling constants and the degrees of freedom independent of the nuisance parameters. This demonstrates that the Wilks phenomenon continues to hold under a variety of smoothing techniques and more relaxed models with unspecified error distributions. We further prove that the GLR tests are asymptotically optimal in terms of rates of convergence for nonparametric hypothesis testing. In addition, for testing a parametric additive model, we propose a bias corrected method to improve the performance of the GLR. The bias-corrected test is shown to share the Wilks type of property. Simulations are conducted to demonstrate the Wilks phenomenon and the power of the proposed tests. A real example is used to illustrate the performance of the testing approach.