A Nonparametric Approach to Measuring and Testing Curvature
曲率度量与检验的非参数方法
This article considers the problem of testing curvature (e.g., linearity, concavity, convexity) in a multivariate nonparametric regression model. A measure of curvature, called the simplex statistic, that does not require bandwidth choice and is easy to compute, is introduced. A global test of curvature based on the simplex statistic is also introduced. Localized versions of the test, which require smoothing parameters, are shown to be consistent against more general…