On the uniform consistency of the Hill estimator. Vrije Universiteit Brussel
We start by considering a kernel estimator g_{n,h}(t) for the regression function m_g(t):=E[g(Y)|X=t], where t is fixed and g:R->R is a measurable function with finite second moment. If h=h_n is a deterministic sequence such that h_n->0 and nh_n^d/log log n->\infty, it is well-known that g_{n,h_n}(t) estimates consistently m_g(t)f_X(t), where f_X is the density function of X. As an extension, we present a result in which additional ...