Sequential fixed-width confidence bands for kernel regression estimation
Dharmasena, L. S., de Silva, B. M. and Zeephongsekul, P. 2008, Sequential fixed-width confidence bands for kernel regression estimation, in IMECS 2008 : Proceedings of the International MultiConference of Engineers and Computer Scientists 2008, Newswood Limited / International Association of Engineers, [Kowloon, Hong Kong], pp. 1-5.
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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.
Field of Research
080699 Information Systems not elsewhere classified
Socio Economic Objective
970108 Expanding Knowledge in the Information and Computing Sciences
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