Data-Driven Version of Neyman's Smooth Test of Fit
Neyman平滑拟合优度检验的数据驱动版本AI 解读 ↓
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Neyman平滑拟合优度检验的数据驱动版本
- 研究问题
- Neyman平滑均匀性检验的分量数如何由数据选择，使检验能够适应不同备择，而不依赖事先指定的偏离方向？
- 方法与思路
- 作者将均匀密度嵌入指数族，用 Schwarz 的 BIC 选择模型维数，再以所选维数确定平滑检验的分量数。
- 材料陈述的贡献
- 摘要称证明了该方法的一致性；模拟显示检验能适应所考察的备择，且功效与其他检验相比表现良好。
- 阅读关注点
- 应核对候选维数范围、BIC选择后的检验校准及一致性条件，查看不同备择与样本量下的尺寸和功效比较。
- 阅读边界
- 材料为版本未注明的 OpenAlex 索引摘要；一致性条件、校准方法及模拟数值未提供，不能推断普遍功效优势或刊本变化。
原文摘要
Neyman's smooth test for testing uniformity is a recognized goodness-of-fit procedure. As stated by LaRiccia, the test can be viewed as a compromise between omnibus test procedures, with generally low power in all directions, and procedures whose power is focused in the direction of a specific alternative. The basic idea behind this test is to embed the null density into, say, a k-dimensional exponential family and then to construct an asymptotically optimal test for the parametric testing problem. The resulting procedure is Neyman's test with k components. The most difficult problem related with using this test is the choice of k. Recommendations in statistical literature are sometimes confusing. Some authors advocate a small number of components, whereas others show that in some situations a larger number of components is profitable. All existing suggestions concerning how to select k exploit in fact some preliminary knowledge about a possible alternative. In this article, a new data-driven method for selecting the number of components in Neyman's test is proposed. The method consists of using Schwarz's BIC procedure to choose the dimension of the exponential model for the data and then using the chosen dimension as the number of components. So this novel procedure relies on fitting the model to the data and verifying whether the difference between the model and the uniform distribution is significant. Consistency of the method is proved. Presented simulations show that the test adapts well to the alternative at hand. Simulated power of the data-driven version of Neyman's test also performs well in comparison with that of other tests.