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Sample size determination for kernel regression estimation using sequential fixed-width confidence bands

Dharmasena, L. Sandamali, Zeephongsekul, P. and de Silva, Basil M. 2008, Sample size determination for kernel regression estimation using sequential fixed-width confidence bands, IAENG international journal of applied mathematics, vol. 38, no. 3, pp. 129-135.

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Title Sample size determination for kernel regression estimation using sequential fixed-width confidence bands
Author(s) Dharmasena, L. Sandamali
Zeephongsekul, P.
de Silva, Basil M.
Journal name IAENG international journal of applied mathematics
Volume number 38
Issue number 3
Start page 129
End page 135
Total pages 7
Publisher Newswood Limited / International Association of Engineers
Place of publication Hong Kong, China
Publication date 2008
ISSN 1992-9978
Keyword(s) fixed-width confidence interval
local linear estimator
nadaraya-Watson estimator
nonparametric
regression
purely sequential procedure
random design
two-stage sequential procedure
approximation theory
regression analysis
confidence intervals
nonparametric statistics
bandwidths
statistical hypothesis testing
Summary We consider a random design model based on independent and identically distributed 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 procedures 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 confi dence bands based on the local linear estimator have the better performance than those constructed by using Nadaraya-Watson estimator. However both estimators are shown to have asymptotically correct coverage properties.
Language eng
Field of Research 089999 Information and Computing Sciences not elsewhere classified
Socio Economic Objective 970108 Expanding Knowledge in the Information and Computing Sciences
HERDC Research category C1.1 Refereed article in a scholarly journal
Copyright notice ©2009, Newswood Limited / International Association of Engineers
Persistent URL http://hdl.handle.net/10536/DRO/DU:30033195

Document type: Journal Article
Collections: School of Information and Business Analytics
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