A Cubic Spline Extension of the Durbin-Watson Test
提出一种基于残差平滑性的曲率统计量，用于检验线性回归模型设定错误，对等距数据可简化计算，并推广到不等距观测的广义均方逐次差分统计量，模拟显示在噪声小、模式复杂度适中时功效优于常用检验。
We propose a new test for model misspecification in linear regression, based on a measure of ‘smoothness’ of the regression residuals. This ‘curvature statistic’ is related to a property of cubic splines and leads to a convenient, powerful test for patterns. The distribution of the curvature statistic may be derived from assumptions of normality. For equally spaced data, the calculations are simplified and a table of significance points of the distribution is given. Smoothness considerations also lead to a natural generalization of the Durbin–Watson or mean-square successive differences statistic for unequally spaced observations. This generalized mean-squared successive differences statistic arises when linear splines are substituted for cubic splines in the development of the curvature statistic. The power of the curvature statistic is investigated by simulation. Compared to several other commonly used tests for patterns, the curvature test is shown to be more powerful where noise levels are small and the complexity of the underlying pattern is moderate. The calculation and use of this statistic is illustrated on a problem involving nonlinear regression residuals.