srp.l {srp}

The (simpler) Smooth-Rough Partition linear regression model fitting

Description

This function performs same as srp.c except that constrained functional coefficient is estimated as a linear function.

Usage

srp.l(x, y, maxq = max(30, ceiling(0.1 * dim(x)[1])), plot = T)

Arguments

x

A matrix you wish to fit Smooth-Rough Partition model. The dimension of row is the number of variables which are pre-ordered in terms of their importance in prediction.

y

A vector you wish to use as a response variable in case of regressing y on x. If y is missing, the response variable is obtained from the last row of x.

maxq

An integer specifying the maximum number of unconstrained parameters which the model can have. The default is max(30, ceiling(0.1*dim(x)[1])).

plot

If true, it gives the plot of estimated regression coefficients.

Details

The estimation procedure of Smooth-Rough Partition model is described in "Regularised forecasting via smooth-rough partitioning of the regression coefficients", H. Maeng and P. Fryzlewicz (2018), preprint.

Value

muhat

The estimator of constant parameter.

bhat

The vector of evaluated constrained (linear) functional regression coefficient.

ahat

The vector of unconstrained regression coefficient estimators.

etahat

The vector containing both bhat and ahat with unevaluated form.

yhat

The vector of estimated response variable.

SIC

The vector of Schwarz criterion with length maxq which is computed for the different number of unconstrained parameters.

qhat

The optimal number of unconstrained parameters selected in the model.

Author(s)

Hyeyoung Maeng, [e-mail]

See Also

srp.c, predict.srp.l, sic.l

Examples

x <- matrix(rnorm(10000), ncol=100)
srp.l(x)