Strong consistency of kernel estimates of regression function under dependence

By a classic Tauberian theorem and moment inequalities, strong LrLr-consistency (1≤r<∞)(1≤r<∞) of Nadaraya–Watson regression estimates is established under conditions only on moments together with ρρ-mixing or order of αα-mixing. A similar L1L1-consistency result concerns Rosenblatt–Parzen density estimates, weakening conditions in previous literature.