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Sequential fixed-width confidence bands for kernel regression estimation

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conference contribution
posted on 2008-01-01, 00:00 authored by Lasitha DharmasenaLasitha Dharmasena, B de Silva, P Zeephongsekul
We consider a random design model based on independent and identically distributed (iid) pairs of observations (Xi, Yi), where the regression function m(x) is given by m(x) = E(Yi|Xi = x) with one independent variable. In a nonparametric setting the aim is to produce a reasonable approximation to the unknown function m(x) when we have no precise information about the form of the true density, f(x) of X. We describe an estimation procedure of non-parametric regression model at a given point by some appropriately constructed fixed-width (2d) confidence interval with the confidence coefficient of at least 1−. Here, d(> 0) and 2 (0, 1) are two preassigned values. Fixed-width confidence intervals are developed using both Nadaraya-Watson and local linear kernel estimators of nonparametric regression with data-driven bandwidths.

The sample size was optimized using the purely and two-stage sequential procedure together with asymptotic properties of the Nadaraya-Watson and local linear estimators. A large scale simulation study was performed to compare their coverage accuracy. The numerical results indicate that the confidence bands based on the local linear estimator have the best performance than those constructed by using Nadaraya-Watson estimator. However both estimators are shown to have asymptotically correct coverage properties.



International Conference on Data Mining and Applications (2008 : Kowloon, Hong Kong)


1 - 5


Newswood Limited / International Association of Engineers


Kowloon, Hong Kong

Place of publication

[Kowloon, Hong Kong]

Start date


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Publication classification

E1.1 Full written paper - refereed

Copyright notice

2008, Newswood Limited / International Association of Engineers


S Ao, O Castillo, C Douglas, D Feng, J Lee

Title of proceedings

IMECS 2008 : Proceedings of the International MultiConference of Engineers and Computer Scientists 2008