A test for linear versus convex regression function using shape-restricted regression
利用形状约束回归检验线性与凸回归函数
An unbiased test for the appropriateness of the simple linear regression model is presented. The null hypothesis is that the underlying regression function is indeed a line, and the alternative is that it is convex. The exact distribution for a likelihood ratio test statistic is that of a mixture of beta random variables, with the mixing distribution calculated from relative volumes of polyhedral convex cones determined by the convex shape restriction. Simulations show that…