A Review of the Development and Application of Recursive Residuals in Linear Models
线性模型中递归残差的发展与应用综述AI 解读 ↓
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线性模型中递归残差的发展与应用综述
- 研究问题
- 递归残差的独立性、同方差性和计算顺序依赖如何服务于线性模型检验，并用于发现结构变化及其他模型问题？
- 方法与思路
- 作者综述递归残差的性质、顺序选择和诊断应用，覆盖相关性、异方差、函数误设及异常观测，并讨论模型扩展和计算。
- 材料陈述的贡献
- 摘要归纳递归残差在模型验证中的多种用途，并介绍一般协方差、多元线性与非线性模型中的相关研究及计算程序。
- 阅读关注点
- 应核对独立性与同方差性依赖的模型条件、观测排序的影响，以及结构变化检验和其他诊断统计量的具体构造。
- 阅读边界
- 这是综述，摘要未列出性质成立条件或各诊断的性能比较；不能视为普遍独立性保证，OpenAlex 索引版本未注明。
原文摘要
Recursive residuals have been shown to be useful in a variety of applications in linear models. Unlike the more familiar ordinary least squares residuals or studentized residuals, recursive residuals are independent as well as homoscedastic under the model. Their independence is particularly appealing for use in developing test statistics. They are not uniquely defined; their values depend on the order in which they are calculated, although their properties do not. In some applications one can exploit this order dependence, coupled with the fact that they are in clear one-to-one correspondence with the observations for which they are calculated. Uses for recursive residuals have been suggested in almost all areas of regression model validation. Regression diagnostics have been constructed from recursive residuals for detecting serial correlation, heteroscedasticity, functional misspecification, and structural change. Other statistics based on recursive residuals have focused on detection of outliers or observations that are influential or have high leverage. Recent work has explored properties and possible uses of recursive residuals in models with a general covariance matrix, multivariate linear models, and nonlinear models. Computing routines are available for obtaining recursive residuals accurately and efficiently.