9 papers
Bias Reduction for Local Polynomial Derivative Estimation
Fujia Chang, W. John Braun
Local polynomial smoothing is commonly used in non-parametric regression, but local linear derivative estimation still has a bias of order . This paper proposes an iterativ…
Nonparametric Estimation under General Nonlinear ODE Constraints: A Comparison with Parametric ODE-Fitting Methods
Chunlei Ge, W. John Braun
Many physical, biological, and epidemiological processes are governed by ordinary differential equations (ODEs) that are nonlinear in the state variable, including logistic populat…
Local Quasi-Linear Models: Kernel Differential Equation Regression and Fire Data Analysis
Chunlei Ge, W. John Braun
We introduce the local quasi-linear (LQL) model, a differential equation-constrained local polynomial regression framework for the general first-order linear ordinary differential…
Differential Equation-Constrained Exponential-Type Local Polynomial Regression Under Model Misspecification
Chunlei Ge, W. John Braun
The issue of model misspecification is critical, yet it is often regarded as unavoidable in applied statistical modeling. Model misspecification can be mitigated by incorporating i…
Differential Equation-Constrained Local Regression for Data with Sparse Design
Chunlei Ge, W. John Braun
Local polynomial regression of order one or higher often performs poorly in areas with sparse data. In contrast, local constant regression tends to be more robust in these regions,…
On Data Sharpening in Nonparametric Autoregressive Models
Simon Snyman, Lengyi Han, W. John Braun
Data sharpening has been shown to reduce bias in nonparametric regression and density estimation. Its performance on nonlinear first order autoregressive models is studied theoreti…
Local Quasi-Exponential Growth Models: Kernel Differential Equation Regression and Mouse Tumor Growth Data
Chunlei Ge, W. John Braun
Local polynomial regression faces several challenges when dealing with sparse data. The difficulty in capturing local features of the underlying function can lead to a possible mis…
The importance of exploration: Modelling site-constant foraging
Sarah A. MacQueen, Clara F. Hardy, W. John Braun +1
Foraging site constancy, or repeated return to the same foraging location, is a foraging strategy used by many species to decrease uncertainty, but it is often unclear exactly how…
Quick and Simple Kernel Differential Equation Regression Estimators for Data with Sparse Design
Chunlei Ge, W. John Braun
Local polynomial regression of order at least one often performs poorly in regions of sparse data. Local constant regression is exceptional in this regard, though it is the least a…