simcurve_smooth_normerr: Simulated data set

In bbefkr: Bayesian bandwidth estimation and semi-metric selection for the functional kernel regression with unknown error density

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

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-π \times t_j+2/9π^2), where t represents the function support range and 0≤q t_1≤q t_2…≤q π 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 τ=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

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.

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)

Example output

Loading required package: splines
Warning message:
In data(simcurve_normerr) : data set ‘simcurve_normerr’ not found

bbefkr documentation built on May 2, 2019, 3:04 a.m.