Adaptive Function-on-Scalar Smoothing Elastic Net
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AFSSEN

Adaptive Function-on-Scalar Smoothing Elastic Net

AFSSEN is a methodology that simultaneously select significant predicotrs and produce smooth estimates of their parameters in a function-on-scalar linear modelwith sub-Gaussian errors and high-dimensional predictors.



Documentation

For installing this package, use

devtools::install_github("ardeeshany/AFSSEN")

AFSSEN.R

We have option to control sparsity and smoothness separately with using two penalty parameters $\lambda_H$ and $\lambda_K$. We aim to estimate a smooth version of $\bf{\beta}$ to minimize the following target function.



![equation](http://latex.codecogs.com/gif.latex?L_%7B%5Clambda%7D%28%5Cbeta%29%3D%5Cdfrac%7B1%7D%7B2N%7D%20%5C%7C%5Cbf%7BY%7D-%5Cbf%7BX%7D%5Cbf%7B%5Cbeta%7D%5C%7C_%7B%5Cmathbb%7BH%7D%7D%5E2+%5Cfrac%7B%5Clambda_%7BK%7D%7D%7B2%7D%20%5Csum_%7Bi%3D1%7D%5E%7BI%7D%20%5C%7CL%28%5Cbeta_%7Bi%7D%29%5C%7C_%7B%5Cmathbb%7BK%7D%7D%5E2%20+%20%5Clambda_%7BH%7D%20%5Csum_%7Bi%3D1%7D%5E%7BI%7D%20%5Ctilde%7Bw%7D_%7Bi%7D%20%5C%7C%20%5Cbeta_%7Bi%7D%5C%7C_%7B%5Cmathbb%7BH%7D%7D)

The following AFFSEN() function helps us to estimate the smooth $\bf{\beta}$ and find the significant predictors:

![alt text](https://github.com/ardeeshany/AFSSEN/blob/master/inst/doc/AFSSEN.png)