Nonparametric Regression Models and Bootstrap Inference
Ella Revzin
Abstract
Ella Revzin
Abstract
This dissertation thesis presents three essays on nonparametric regression and the bootstrap. In the first study, simultaneous confidence bands for univariate conditional mean regression are developed using a bootstrap of polynomial spline regression. The second study extend the work of the first to quasi-likelihood estimation of GLM regression using Free-knot splines. The third study presents a methodological treatment of how to construct tumor growth reference curves using quantile regression.
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This dissertation thesis presents three essays on nonparametric regression and the bootstrap. In the first study, simultaneous confidence bands for univariate conditional mean regression are developed using a bootstrap of polynomial spline regression. The second study extend the work of the first to quasi-likelihood estimation of GLM regression using Free-knot splines. The third study presents a methodological treatment of how to construct tumor growth reference curves using quantile regression.
Key concepts: Statistics, Nonparametric regression, Quantile regression, Polynomial regression, Mathematics, Nonparametric statistics, Regression analysis, Univariate