A Bias Bound Approach to Non-Parametric Inference
Bias bound approach for conditional expectation estimation
Bias bound approach for density estimation
Create a configuration object for bias bound estimations
Create kernel functions based on configuration
Cross-Validation for Bandwidth Selection
The Path to the Data Folder
Fourier Transform Epanechnikov Kernel
Epanechnikov Kernel
The Path to the External Data Folder for Non-R Data Files
Approximation Function for Intensive Calculations
Generate Sample Data
Kernel point estimation
Kernel point estimation
Compute log sample average of fourier transform and get mod
Compute Sample Average of Fourier Transform Magnitude
get the conditional variance of Y on X for given x
get the estimation of A and r
get the estimation of B
Estimation of bias b1x
Estimation of bias byx
get the estimation of Vy
Estimation of sigma_yx
Estimation of sigma
get xi interval
Kernel Regression function
Fourier Transform of Normal Kernel
Normal Kernel Function
Plot the Fourier Transform
Generate n samples from the distribution
Select Optimal Bandwidth
Silverman's Rule of Thumb for Bandwidth Selection
Define the closed form FT of the infinite order kernel sin(x)/(pi*x)
Infinite Kernel Function
True density of 2-fold uniform distribution
Define the Fourier transform of a infinite kernel proposed in Schennac...
Define the inverse Fourier transform function of W
A novel bias-bound approach for non-parametric inference is introduced, focusing on both density and conditional expectation estimation. It constructs valid confidence intervals that account for the presence of a non-negligible bias and thus make it possible to perform inference with optimal mean squared error minimizing bandwidths. This package is based on Schennach (2020) <doi:10.1093/restud/rdz065>.