R packages:

•  A.  FRegSigCom (Functional Regression using Signal Compression Approach). Current version: 0.3.0. The pdf manual is here. This package implements:

           (a). the signal compression approach for linear function-on-function regression proposed in the following paper (1);
           (b). the method for nonlinear function-on-function regression model proposed in the following paper (2);
           (c). the smooth-sparse approach for linear function-on-function regression model in the following paper (3), where the number of predictor curves can be much larger than the sample size;
           (d). the interaction function-on-function regression model and stepwise model selection in the following paper (4).
The pdf manual is here.
           (e). the methods for scalar-on-function and function-on-function regression models with densely observed spiky functional data in the paper (5).
           (f). the methods for functional regression models with multivariate response and multiple or even thousands of predictor curves in the paper (6).
           (g). the methods for function-on-function regression models using wavelet transformation in the paper (7).

     Reference:

• • • (1). Ruiyan Luo and Xin Qi (2017) Function-on-function linear regression by signal compression.  Journal of American Statistical Association. 112(518): 690-705.
    • (2). Xin Qi and Ruiyan Luo. (2019) Nonlinear additive function on function with multiple predictor curves. Statistica Sinica, 29, 719-739.
    • (3). Xin Qi, and Ruiyan Luo. (2018)  Function on function regression with thousands of predictive curves. Journal of Multivariate Analysis, 163: 51-66.
    • (4). Ruiyan Luo and Xin Qi. (2019) Interaction model and model selection for function-on-function regression. Journal of Computational and Graphical Statistics, Volume 28, Issue 2, 309-322.
    • (5). Xin Qi and Ruiyan Luo. Functional regression for highly densely observed data with novel regularization. (Under review).
    • (6). Xin Qi and Ruiyan Luo, Functional regression with multivariate response. (Under review).  
    • (7). Ruiyan Luo  and Xin Qi. (2016) Functional wavelet regression for function-on-function linear models. Electronic Journal of Statistics. 10(2): 3179-3216

•  B.   SiER (Signal Extraction Approach for Sparse Multivariate Response Regression). This package implements  the signal extraction approach for linear  regression proposed in the following paper, where the predictor is a high-dimensional multivariate variable and the response is either a scalar variable or a multivariate variable.  The pdf manual is here.
  Reference:
  • • • Ruiyan Luo and Xin Qi. (2017) Signal extraction approach for sparse multivariate response regression. Journal of Multivariate Analysis. 153: 83–97.

R codes:

1. 1. Wavelet based signal compression for linear function-on-function regression (zip file here). This file contains the R code for all the R functions, simulations  and applications to real data in the following paper. We implement a wavelet based method for function-on-function regression model, where we apply wavelet transformation to  multiple predictor curves and convert the function-on-function regression to the function on high-dimensional multivariate wavelet coefficients regression.
      Reference:
      •  Ruiyan Luo, and Xin Qi.(2016) Functional wavelet regression for function-on-function linear models. Electronic Journal of Statistics. 10(2):3179-3216.
   2.