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Nonparametric Estimation of a Regression Function: Limiting Distribution 2
Author(s) -
Cheng KuangFu,
Lin PiErh
Publication year - 1981
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1981.tb00776.x
Subject(s) - estimator , isotonic regression , mathematics , limiting , consistency (knowledge bases) , regression , nonparametric regression , asymptotic distribution , statistics , regression function , nonparametric statistics , function (biology) , regression analysis , combinatorics , discrete mathematics , mechanical engineering , evolutionary biology , engineering , biology
Summary Consider the regression model Y i = g( x i ) + e i , i = 1,…, n, where g is an unknown function defined on [0, 1], 0 = x 0 < x 1 < … < x n ≤ 1 are chosen so that max 1≤i≤n (x i ‐x i‐ 1 ) = 0(n ‐1 ), and where {e i } are i.i.d. with Ee 1 = 0 and Var e 1 ‐ s̀ 2 . In a previous paper, Cheng & Lin (1979) study three estimators of g, namely, g 1n of Cheng & Lin (1979), g 2n of Clark (1977), and g 3n of Priestley & Chao (1972). Consistency results are established and rates of strong uniform convergence are obtained. In the current investigation the limiting distribution of & in , i = 1, 2, 3, and that of the isotonic estimator g** n are considered.