Note on the uniform convergence of density estimates for mixing random variables (Q578794)

For a stationary sequence \((X_ n\), \(n\geq 0)\) of random variables the authors prove almost sure convergence results for the (usual) density estimators \(\hat f_ n(x)=n^{-1}h_ n^{-t}\sum^{n}_{j=1}K((x- X_ j)h_ n^{-1})\) under various assumptions on \(h_ n\), t and K and under different mixing assumptions on the \(X_ i's\). An application to Markov processes is also included.