semimrGen function

Semiparametric Mixture Data Generator

`semimrGen' is used to generate data for a two-component semiparametric mixture of regression models: [REMOVE_ME]$p m_1(x) + (1-p) m_2(x), [REMOVE_ME_2]$

where $m_1(x) = 4 -\sin(2\pi x)$ and $m_2(x) = 1.5 + \cos(3\pi x).$

This function is used in the examples for the semimrLocal and semimrGlobal functions. See the examples for details.

semimrGen(n, p = 0.5, var = c(.1, .1), u)

Arguments

• n: a scalar, specifying the number of observations in $x$.
• p: a scalar, specifying the probability of an observation belonging to the first component, i.e., $p$ in the model.
• var: a vector of variances of observations for the two components.
• u: a vector of grid points for $x$. If some specific explanatory variable are needed, create a vector and assign to u.

Returns

A list containing the following elements: - x: vector of length n, which represents the explanatory variable that is randomly generated from Uniform(0,1).

• y: vector of length n, which represent the response variable that is generated based on the mean functions $m_1(x)$ and $m_2(x)$, with the addition of normal errors having a mean of 0 and a standard deviation specified by the user.

• true_mu: n by 2 matrix containing the values of $m_1(x)$ and $m_2(x)$ at x.

• true_mu_u: length(u) by 2 matrix containing the values of $m_1(x)$ and $m_2(x)$ at u.

Description

`semimrGen' is used to generate data for a two-component semiparametric mixture of regression models:

where $m_1(x) = 4 -\sin(2\pi x)$ and $m_2(x) = 1.5 + \cos(3\pi x).$

This function is used in the examples for the semimrLocal and semimrGlobal functions. See the examples for details.

Examples

n = 100
u = seq(from = 0, to = 1, length = 100)
true_p = c(0.3, 0.7)
true_var = c(0.09, 0.16)
out = semimrGen(n = n, p = true_p[1], var = true_var, u = u)

See Also

semimrLocal, semimrGlobal, semimrBinFull