Date of Award
Doctor of Philosophy
Kris De Brabanter
Nonparametric methods are popular in data analysis since it requires few assumptions about the underlying populations that the data are coming from, e.g. nonparametric regression and nonparametric density estimation. Nonparametric regression drew a lot of attention since mid sixties and it is well studied because it provides the possibility to uncover the nonlinear relationship between a dependent variable and one or more independent variables without imposing the assumption on the shape of the mean function. We propose simultaneous confidence intervals for the estimated regression curve using nonparametric methods. We also propose a nonparametric derivative estimation method and apply the nonparametric method in bloodstain pattern analysis.
First, we study the convergence rate of simultaneous bias corrected confidence intervals for a smooth curve using local polynomial regression which is a well-known nonparametric regression technique in the area of statistics. We extend the idea of volume-of-tube to construct the simultaneous confidence intervals for this biased estimator. We empirically show that the proposed simultaneous confidence intervals attain, at least approximately, nominal coverage.
Second we propose nonparametric first and second order derivative estimators without having to estimate the regression function. The estimator is based on a variance-reducing linear combination of symmetric difference quotients. We establish the asymptotic properties of the proposed derivative estimators and propose fast tuning methods to select parameters. We compare the proposed estimators with popular estimators for derivative estimation such as local polynomial regression and smoothing
Last we apply the nonparametric methods to construct the features in classification of bloodstain patterns. Bloodstain pattern analysis (BPA) plays an important role in forensics towards crime scene analysis. We propose an automated framework to classify the bloodstain spatters caused by either
gunshot or blunt impact, based on machine learning methods. We analyze 94 blood spatters which are being disseminated as free public datasets for research purposes and construct features using nonparametric methods. The study
also shows how the distance between the target surface collecting the stains and the blood source influences the bloodstain pattern.
Finally we obtain the accuracy of the proposed classification model for different distances ranges.
Liu, Yu, "Nonparametric curve estimation and applications" (2019). Graduate Theses and Dissertations. 17248.
Available for download on Friday, April 02, 2021