bbefkr (version 4.2)

simcurve_smooth_normerr: Simulated data set

Description

Simulated data

Usage

data(simcurve_smooth_normerr)

Format

simcurve_smooth_normerr: 50 by 100 simcurve_rough_normerr: 50 by 100 simresp_normerr: 50 by 1 tau_normerr: 50 by 1

Source

H. L. Shang (2013) Bayesian bandwidth estimation for a nonparametric functional regression model with unknown error density, Computational Statistics and Data Analysis, 67, 185-198.

Details

The simulated discretised curves are defined as $x_i(t_j) = a_i cos(2t_j)+b_isin(4t_j)+c_i(t_j^2-\pi \times t_j+2/9\pi^2)$, where t represents the function support range and $0\leq t_1\leq t_2\dots\leq \pi$ are equispaced points within the function support range, $a_i$, $b_i$ and $c_i$ are independently drawn from a uniform distribution on [0,1], and $n$ represents the sample size. For simulating a set of rough curves, we add one extra term $d_j$ generated from $U(-0.1, 0.1)$. Having defined functional curves, we then construct the regression mean function $\tau=10\times (a_i^2-b_i^2)$. Then the response variable is obtained by adding the regression mean function with a set of errors generated from a standard normal distribution

References

H. L. Shang (2013) Bayesian bandwidth estimation for a semi-functional partial linear regression model with unknown error density, Computational Statistics, in press.

H. L. Shang (2013) Bayesian bandwidth estimation for a nonparametric functional regression model with unknown error density, Computational Statistics and Data Analysis, 67, 185-198.

F. Ferraty, I. Van Keilegom, P. Vieu (2010) On the validity of the bootstrap in non-parametric functional regression, Scandinavian Journal of Statistics, 37(2), 286-306.

Examples

data(simcurve_normerr)