r.cfs.2003: Utilities for the simulation of functional linear models

In egarpor/rp.flm.test: Goodness-of-fit Test for the Functional Linear Model with Scalar Response Based on Random Projections

Description

The functions r.cfs.2003, r.hh.2006 and r.bridge sample the functional covariate and construct functional coefficients for their use in functional linear models:

• r.cfs.2003 implements examples (a) and (b) in Section 5 of Cardot et al. (2003).

• r.hh.2006 gives models (i), (ii) and (iii) in Section 5 of Hall and Hosseini-Nasab (2006).

• r.bridge samples a Brownian motion and creates a functional coefficient constructed from the eigenfunctions √2 * sin(k*t*π).

Usage

r.cfs.2003(n, t = seq(0, 1, len = 201), b = c(2, 4, 5)/sqrt(2),
  type = c("a", "b")[1])

r.hh.2006(n, t = seq(0, 1, len = 201), imod = 1)

r.bridge(n, t = seq(0, 1, len = 201), b = c(2, 4, 5)/sqrt(2))

Arguments

n	number of functions to sample.
t	time locations for the functional data.
b	coefficients of the functional coefficient in the theoretical basis of principal components of the Brownian motion.
type	either example "a" or "b" from Cardot et al. (2003).
imod	either 1, 2 or 3 for denoting models (i), (ii) and (iii) in Hall and Hosseini-Nasab (2006).

Value

A list with the following elements:

X.fdata

the sample of functional data, an fdata object of length n.

beta.fdata

the functional coefficient, an fdata object.

Author(s)

Manuel Febrero-Bande ([e-mail]) and Eduardo García-Portugués ([e-mail]).

References

Cardot, H., Ferraty, F., Sarda, P. (2003) Spline estimators for the functional linear model. Statistica Sinica, 13(3), 571–592. http://www3.stat.sinica.edu.tw/statistica/oldpdf/a13n31.pdf

Hall, P. and Hosseini-Nasab, M. (2006) On properties of functional principal components analysis. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 68(1), 109–126. http://dx.doi.org/10.1111/j.1467-9868.2005.00535.x

Examples

# Cardot et al. (2003)
plot(r.cfs.2003(n = 100, type = "a")$X.fdata)
plot(r.cfs.2003(n = 100, type = "b")$X.fdata)

# Hall and Hosseini-Nasab (2006)
plot(r.hh.2006(n = 100, imod = 1)$X.fdata)
plot(r.hh.2006(n = 100, imod = 2)$X.fdata)
plot(r.hh.2006(n = 100, imod = 3)$X.fdata)

# Sample bridge
plot(r.bridge(n = 100)$X.fdata)

egarpor/rp.flm.test documentation built on Oct. 20, 2021, 12:31 a.m.