The problem considered relates to estimating an arbitrary regression function m(x) from sample pairs (Xᵢ,Yᵢ) 1 ≤ i ≤ n. A model is assumed of the form Y = m(x) + ε(x) where ε(x) is a random variable with expectation 0. One well known method for estimating m(x) is by using one of a class of kernel regression estimators say m(n)(x). Schuster (1972) has shown conditions under which the limiting distribution of the kernel estimator m(n)(x) is the normal distribution. It might also be of interest to use the data to estimate the distribution of m(n)(x). One could, given this estimate, construct approximate confidence bounds for the function m(x). Three estimators are proposed for the density of m(n)(x). They share a basis in non-parametric kernel regression and utilize bootstrap techniques to obtain the density estimate. The order of convergence of one of the estimators is examined and conditions are given under which the order is higher then when estimation is by the normal approximation. Finally the performance of each estimator for constructing confidence bounds is compared for moderate sample sizes using computer studies.
| Identifer | oai:union.ndltd.org:arizona.edu/oai:arizona.openrepository.com:10150/183923 |
| Date | January 1986 |
| Creators | RUTHERFORD, BRIAN MILNE. |
| Contributors | Yakowitz, Sidney |
| Publisher | The University of Arizona. |
| Source Sets | University of Arizona |
| Language | English |
| Detected Language | English |
| Type | text, Dissertation-Reproduction (electronic) |
| Rights | Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. |
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