Robust testing for superiority between two regression curves
نویسندگان
چکیده
where mj : R → R is a nonparametric smooth function and the error εj is independent of the covariate Xj. As is usual in a robust framework, we will assume that the errors εj are such that εj = σj Uj, where Uj has a symmetric distribution Gj(·) with scale 1, so that we are able to identify the error’s scale, σj. When second moments exist, as it is the case of the classical approach, these conditions imply that E(εj) = 0 and Var(εj) = σ j , which means that mj represents the conditional mean, while σ j equals the residuals variance, i.e., σ 2 j = Var(Yj −mj(Xj)). The nonparametric nature of model (??) offers more flexibility than the standard linear model when modelling a complicated relationship between the response variable and the covariate. In many situations, it is of interest to compare the regression functions m1 and m2 to decide if the same functional form appears in both populations. In particular, we will focus on testing the null hypothesis of equality of the regression curves versus a one-sided alternative. Let R be the common support of the covariates X1 and X2 where the comparison will be performed. The null hypothesis to be considered is H0 : m1(x) = m2(x) for all x ∈ R,
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ورودعنوان ژورنال:
- Computational Statistics & Data Analysis
دوره 97 شماره
صفحات -
تاریخ انتشار 2016