Model checks for regression under alpha-mixing

We study the local and global behaviors of regression splines under -mixing.The asymptotic normality for the regression splines is established.We also prove a central limit theorem for integrated square error of least squares splines estimators.We investigate the limit distribution of the same functional when we substitute a constrained estimator for the regression function.In addition, results on the maximal deviation for some derivatives of the estimators are provided, which leads to the construction of goodness-of-t-tests and testing the monotonicity or the convexity of the regression function.We prove that the tests are consistent and have power against some local alternatives.