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The application of B-spline smoothin...

Wang, Jing.

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The application of B-spline smoothing: Confidence bands and additive modelling.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	The application of B-spline smoothing: Confidence bands and additive modelling./
作者:	Wang, Jing.
面頁冊數:	146 p.
附註:	Source: Dissertation Abstracts International, Volume: 67-10, Section: B, page: 5831.
Contained By:	Dissertation Abstracts International67-10B.
標題:	Statistics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3236448
ISBN:	9780542910234

The application of B-spline smoothing: Confidence bands and additive modelling.
Wang, Jing.

The application of B-spline smoothing: Confidence bands and additive modelling. - 146 p.

Source: Dissertation Abstracts International, Volume: 67-10, Section: B, page: 5831.

Thesis (Ph.D.)--Michigan State University, 2006.

Asymptotically exact and conservative confidence bands are obtained for nonparametric regression function, based on constant and linear polynomial spline estimation, respectively. Compared to the pointwise nonparametric confidence interval of Huang (2003), the confidence bands are inflated only by a factor of {log (n)}1/2, similar to the Nadaraya-Watson confidence bands of Hardle (1989), and the local polynomial bands of Xia (1998) and Claeskens and Van Keilegom (2003). Simulation experiments have provided strong evidence that corroborates with the asymptotic theory.

ISBN: 9780542910234Subjects--Topical Terms:

517247
Statistics.

The application of B-spline smoothing: Confidence bands and additive modelling.
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502 $a Thesis (Ph.D.)--Michigan State University, 2006.
520 $a Asymptotically exact and conservative confidence bands are obtained for nonparametric regression function, based on constant and linear polynomial spline estimation, respectively. Compared to the pointwise nonparametric confidence interval of Huang (2003), the confidence bands are inflated only by a factor of {log (n)}1/2, similar to the Nadaraya-Watson confidence bands of Hardle (1989), and the local polynomial bands of Xia (1998) and Claeskens and Van Keilegom (2003). Simulation experiments have provided strong evidence that corroborates with the asymptotic theory.
520 $a A great deal of effort has been devoted to the inference of additive model in the last decade. Among the many existing procedures, the kernel type are too costly to implement for large number of variables or for large sample sizes, while the spline type provide no asymptotic distribution or any measure of uniform accuracy. We propose a synthetic estimator of the component function in an additive regression model, using a one-step backfitting, with spline smoothing in the first stage and kernel smoothing in the second stage. Under very mild conditions, the proposed SBK estimator of the component function is asymptotically equivalent to an ordinary univariate Watson estimator, hence the dimension is effectively reduced to one at any point. This dimension reduction holds uniformly over an interval under stronger assumptions of normal errors, and asymptotic simultaneous confidence bands are provided for the component functions. Monte Carlo evidence supports the asymptotic results for dimensions ranging from low to very high, and sample sizes ranging from moderate to large. The proposed simultaneous confidence bands are applied to the Boston housing data for linearity diagnosis.
520 $a Phenological information reflecting seasonal changes in vegetation is an important input variable in climate models such as the Regional Atmospheric Modeling System (RAMS). It varies not only among different vegetation types but also with geographic locations (latitude and longitude). In the current version of RAMS, phenologies are treated as a simple sine function that is solely related to the day of year and latitude, in spite of major seasonal variability in precipitation and temperature. In short, the sine curves of phenology are far different from the observed. Via linear spline smoothing we developed more realistic phenological functions of all land covers in the East Africa to improve RAMS model based on remote sensing observations. In addition, we quantify the differences between the RAMS's default phenological curves and those linear spline estimates derived from remote sensing observations.
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