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Nonparametric Regression Models and Bootstrap Inference

Ella Revzin

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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.

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Available 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.

Key concepts: Statistics, Nonparametric regression, Quantile regression, Polynomial regression, Mathematics, Nonparametric statistics, Regression analysis, Univariate

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