simulation: Function-on-Scalar linear model data, used to test FLAME...

In ardeeshany/FLAME: FLAME for high-dimensional Function-on-Scalar regression problems

Description

Data of a Function-on-Scalar linear model, it includes the design matrix, the time domain, the response functions (both as pointwise evaluations on the time domain, as projections on the kernel basis, and as fd objects), the true coefficients of the Function-on-Scalar model and the Gaussian errors.

Usage

data("simulation")

Format

A set of variables associated to the Function-on-Scalar linear model.

• X matrix. N \times I design matrix.

• Y_matrix matrix. J \times N matrix containing the N response functions projected on the J-dimensional kernel basis.

• T_domain vector. m-length vector of the time domain where the response functions are evaluated.

• Y_full matrix. N \times m matrix containing the response functions evaluated on the T_domain grid.

• Y_fd fd object. N-length fd object of the repsonse functions. The same response functions as Y_matrix and Y_full, but projected on a 20 elements cubic Bspline basis.

• B_true matrix. J \times I0 matrix of the projection on the kernel basis of the I0 significant predictor coefficients.

• eps matrix. N \times m matrix of the random errors added to the model. Evaluation of the N functions on the m-dimensional time domain.

Details

It contains data on a high-dimensional simulation setting with N = 500 and I = 1000 to highlight both the efficiency of FLAME in estimation and in variable selection. Only I0 = 10 predictors, in fact, are meaningful for the response, the others have a null effect on the Y's.

The predictor matrix X is the standardized version of a matrix randomly sampled from a N dimension Gaussian distribution with 0 average and identity covariance matrix. The true coefficients β are sampled from a Matern process with 0 average and parameters (ν = 2.5, \textrm{range} = 1/4, σ^2=1).

Observations y(t) are, then, obtained as the sum of the contribution of all the predictors and a random noise eps, a 0-mean Matern process with parameters (ν = 1.5, \textrm{range} = 1/4, σ^2=1). Functions are sampled on a m = 50 points grid.

See covMaterniso for details on the covariance structure of coefficients and errors.

Examples

data(simulation)

ardeeshany/FLAME documentation built on May 14, 2019, 8:41 a.m.