 Fixed-design nonparametric regression

The fixed-design nonparametric regression model observes $Y_i=m(x_i)+\sigma {ϵ}_i$ at deterministic design points $x_i$. For independent and identically distributed random variables ${ϵ}_i$ with the standard normal distribution, comparing two mean functions has Kullback-Leibler divergence ${\sum }_i(m_1(x_i)-m_0(x_i){)}^2/(2{\sigma }^2)$.