In some applications, we require a monotone estimate of a regression function. In others, we want to test whether the regression function is monotone. For solving the first problem, Ramsay's, Kelly and Rice's, as well as point-wise monotone regression
functions in a spline space are discussed and their properties developed. Three monotone estimates are defined: least-square regression splines, smoothing splines and binomial regression splines. The three estimates depend upon a "smoothing parameter":
the number and location of knots in regression splines and the usual [formula omitted] in smoothing splines. Two standard techniques for choosing the smoothing parameter, GCV and AIC, are modified for monotone estimation, for the normal errors case. For answering the second question, a test statistic is proposed and its null distribution conjectured. Simulations are carried out to check the conjecture. These techniques are applied to two data sets. / Science, Faculty of / Statistics, Department of / Graduate
| Identifer | oai:union.ndltd.org:UBC/oai:circle.library.ubc.ca:2429/29457 |
| Date | January 1990 |
| Creators | Zuo, Yanling |
| Publisher | University of British Columbia |
| Source Sets | University of British Columbia |
| Language | English |
| Detected Language | English |
| Type | Text, Thesis/Dissertation |
| Rights | For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. |
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