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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).
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참고문헌 (24)
참고문헌 신청
A. A. Georgiev / 1985 / Local properties of function fitting estimates with application to system identification, Mathematical statistics and applications, Vol. B (Bad Tatzmannsdorf, 198
A. A. Georgiev / 1986 / Nonparametric function recovering from noisy observations / Journal of Statistical Planning and Inference 13 (1) : 1 ~ 14
A. A. Georgiev / 1988 / Consistent nonparametric multiple regression: the fixed design case / Journal of Multivariate Analysis 25 (1) : 100 ~ 110
G. G. Roussas / 1989 / Consistent regression estimation with fixed design points under dependence conditions / Statistics & Probability Letters 8 (1) : 41 ~ 50
G. G. Roussas / 1992 / Fixed design regression for time series: asymptotic normality / Journal of Multivariate Analysis 40 (2) : 262 ~ 291
A. A. Georgiev / 1986 / Nonparametric function recovering from noisy observations / Journal of Statistical Planning and Inference 13 (1) : 1 ~ 14
A. A. Georgiev / 1988 / Consistent nonparametric multiple regression: the fixed design case / Journal of Multivariate Analysis 25 (1) : 100 ~ 110
G. G. Roussas / 1989 / Consistent regression estimation with fixed design points under dependence conditions / Statistics & Probability Letters 8 (1) : 41 ~ 50
G. G. Roussas / 1992 / Fixed design regression for time series: asymptotic normality / Journal of Multivariate Analysis 40 (2) : 262 ~ 291
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