Asymptotically Minimax Goodness-of-fit Testing for Single-index Models

In the context of non parametric multivariate regression model, we are interested in goodness-of-fit testing for single-index models. These models dimension reduction and therefore useful multidimensional nonparametric statistics because well-known phenomenon called curse dimensionality. Fan Li [5] have proposed first consistent test by using kernel estimation method a central limit theorem degenerate -statistics order higher than two. Since then, minimax properties this not been investigated. Following work, use here asymptotic approach. We finding rate src=image/13427297_01.gif> which gives minimal distance between null alternative hypotheses such that successful is possible. propose procedure level src=image/13427297_02.gif> can tend to zero when sample size tends infinity. established our showing it reaches src=image/13427297_03.gif> there no reaching src=image/13427297_04.gif>. Because its properties, able distinguish hypothesis closest possible alternative. The results obtained were thanks large deviation result U-statistic two appearing decision variable.