The Asymptotic Variance of the Continuous-Time Kernel Estimator with Applications to Bandwidth Selection

摘要: We derive simple expressions for the asymptotic variance of kernel-density estimator a stationary continuous-time process in one and d dimensions relate convergence rates to sample path smoothness. Important applications include methods selecting optimal smoothing parameters construction confidence bands testing hypotheses about density. In simulation study results are applied bandwidth selection discrete-time processes that can be modelled as sampled at high rate.