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A Berry-Esseen type bound of regression estimator based on linear process errors

Han-Ying Liang|Yu-Yu Li
대한수학회 (The Korean Mathematical Society)|2008.11|대한수학회지 (Journal of the KMS)|제45권 제6호|pp. 1753-1767

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참고문헌

키워드

nonparametric regression modelnegatively associated random variableBerry-Esseen type bound.
주제분류수학

초록

Consider the nonparametric regression model Yni = g(xni)+ ∈ni (1 ≤ i ≤ n), where g(·) is an unknown regression function, xni are known fixed design points, and the correlated errors {∈ni, 1 ≤ i ≤ n} have the same distribution as {Vi, 1 ≤ i ≤ n}, here Vt = [수식] with [수식] 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).

Abstract

Consider the nonparametric regression model Yni = g(xni)+ ∈ni (1 ≤ i ≤ n), where g(·) is an unknown regression function, xni are known fixed design points, and the correlated errors {∈ni, 1 ≤ i ≤ n} have the same distribution as {Vi, 1 ≤ i ≤ n}, here Vt = [수식] with [수식] 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).

참고문헌 (27)

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