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Confidence Intervals Based on Local Linear Smoother
Author(s) -
CHEN SONG XI,
QIN YONG SONG
Publication year - 2002
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/1467-9469.00273
Subject(s) - mathematics , coverage probability , confidence interval , boundary (topology) , confidence region , statistics , linear regression , confidence distribution , parametric statistics , function (biology) , mathematical analysis , evolutionary biology , biology
Point‐wise confidence intervals for a non‐parametric regression function in conjunction with the popular local linear smoother are considered. The confidence intervals are based on the asymptotic normal distribution of the local linear smoother. Their coverage accuracy is evaluated by developing Edgeworth expansion for the coverage probability. It is found that the coverage error near the boundary of the support of the regression function is of a larger order than that in the interior, which implies that the local linear smoother is not adaptive to the boundary in terms of coverage. This is quite unexpected as the local linear smoother is adaptive to the boundary in terms of the mean squared error.