A Nonparametric Approach to Measuring and Testing Curvature
提出一种无需带宽选择的曲率度量（单纯形统计量），并构建全局和局部检验，用于多元非参数回归模型中的线性、凹凸性检验，并应用于经验收入曲线和共同基金风格择时分析。
AbstractThis 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 alternatives than the global test. In the univariate case, the local test of concavity (convexity) is consistent against all nonconcave (nonconvex) alternatives. The simplex statistic can also be used in the context of a partially linear regression model. Applications to examining the curvature of the experience-earnings profile and testing the "style timing" of mutual funds are considered.KEY WORDS: ConcavityConvexityNonparametric testU-statistics