This paper is devoted to the study of asymptotic properties of the
regression function kernel estimate in the setting of continuous time
stationary and ergodic data. More precisely, considering the Nadaraya–Watson
type estimator, say m̂
T
(x), of the l-indexed regression function m(x) =𝔼 (l(Y)|X = x) built upon continuous time stationary and ergodic data (X
t
, Y
t
)0≤t≤T
, we establish its pointwise and uniform, over a dilative compact set, convergences with rates. Notice that the ergodic setting covers and completes various situations as compared to the mixing case and stands as more convenient to use in practice.
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