Asymptotic normality of two symmetry test statistics based on the L1-error

In this paper, we propose two new tests to test the symmetry of a distribution. These tests are built up on the asymptotic normality of the L₁-distance to the symmetry of the Kernel and histogram density estimates. A simulation study is carried out to evaluate performances of the kernel based test.     

Kernel regression estimation in a Banach space

In this paper, we study a nonparametric regression estimator when the response variable is in a separable Banach space and the explanatory variable takes values in a separable semi-metric space. Under general conditions, we establish some asymptotic results and give upper bounds for the p$p$-mean and almost sure (pointwise and integrated) estimation errors. Finally, we present the case where the explanatory variable is the Wiener process.