Nonparametric function smoothing: fiducial inference of free knot splines and ecological applications

Nonparametric function estimation has proven to be a useful tool for applied statisticians. Classic techniques such as locally weighted regression and smoothing splines are being used in a variety of circumstances to address questions at the forefront of ecological theory. We first examine an ecological threshold problem and define a threshold as where the derivative of the estimated functions changes states (negative, possibly zero, or positive) and present a graphical method that examines the state changes across a wide interval of smoothing levels. We apply this method to macro-invertabrate data from the Arkansas River. Next we investigate a measurement error model and a generalization of the commonly used regression calibration method whereby a nonparametric function is used instead of a linear function. We present a simulation study to assess the effectiveness of the method and apply the method to a water quality monitoring data set. The possibility of defining thresholds as knot point locations in smoothing splines led to the investigation of the fiducial distribution of free-knot splines. After introducing the theory behind fiducial inference, we then derive conditions sufficient to for asymptotic normality of the multivariate fiducial density. We then derive the fiducial density for an arbitrary degree spline with an arbitrary number of knot points. We then show that free-knot splines of degree 3 or greater satisfy the asymptotic normality conditions. Finally we conduct a simulation study to assess quality of the fiducial solution compared to three other commonly used methods.

Name thesis:degree_name

Doctor of Philosophy (Ph.D.)

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Statistics

Grantor dc:publisher

Colorado State University. Libraries

Year dc:date.issued

2010

Authors dc:creator

• Sonderegger, Derek Lee, author
• Wang, Haonan, advisor
• Hannig, Jan, advisor
• Noon, Barry R. (Barry Richard), 1949-, committee member
• Iyer, Hariharan K., committee member

Statement dc:rights

• Copyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.

Language dc:language.iso

eng, English

Identifier URI

https://doi.org/10.25675/3.018414

Identifier

ETDF2010100001STAT
QA278.8

OAI identifier oai:identifier

oai:mountainscholar.org:10217/39050