A BERRY-ESSEEN TYPE BOUND OF REGRESSION ESTIMATOR BASED ON LINEAR PROCESS ERRORS

Consider the nonparametric regression model Yni = g(xni)+ ϵni (1 ≤ i ≤ n), where g(·) is an unknown regression function, xni are known fixed design points, and the correlated errors {ϵni, 1 ≤ i ≤ n} have the same distribution as {Vi, 1 ≤ i ≤ n}, here Vt = P∞=−∞ ψj et−j with P∞ j=−∞ |ψj | < ∞ and {et} are negatively associated random variables. Under appropriate conditions, we derive a Berry-Esseen type bound for the estimator of g(·). As corollary, by choice of the weights, the Berry- Esseen type bound can attain O(n −1/4 (log n) 3/4 ).

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