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oai:mountainscholar.org:10217/390502025-12-30T03:17:31Zcom_10217_100532com_10217_100000com_10217_100518com_10217_100303col_10217_100538col_10217_100519

Sonderegger, Derek Lee, author Wang, Haonan, advisor Hannig, Jan, advisor Noon, Barry R. (Barry Richard), 1949-, committee member Iyer, Hariharan K., committee member 2007-01-03T05:44:53Z 2007-01-03T05:44:53Z 2010 Sonderegger_colostate_0053A_10025.pdf ETDF2010100001STAT QA278.8 http://hdl.handle.net/10217/39050 https://doi.org/10.25675/3.018414 Department Head: F. Jay Breidt. 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. born digital doctoral dissertations English eng Colorado State University. Libraries 2000-2019 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. Nonparametric function smoothing: fiducial inference of free knot splines and ecological applications Text Doctor of Philosophy (Ph.D.) Doctoral Statistics Colorado State University This Item is protected by copyright and/or related rights (https://rightsstatements.org/vocab/InC/1.0/). You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s). open.access