kdeem.h {MixSemiRob} | R Documentation |
Kernel Density-based EM-type algorithm for Semiparametric Mixture Regression with Unspecified Homogenous Error Distributions
Description
‘kdeem.h’ is used for semiparametric mixture regression using a kernel density-based expectation-maximization (EM)-type algorithm with unspecified homogeneous error distributions (Hunter and Young, 2012).
Usage
kdeem.h(x, y, C = 2, ini = NULL, maxiter = 200)
Arguments
x |
an n by p data matrix where n is the number of observations and p is the number of explanatory variables (including the intercept). |
y |
an n-dimensional vector of response variable. |
C |
number of mixture components. Default is 2. |
ini |
initial values for the parameters. Default is NULL, which obtains the initial values
using the |
maxiter |
maximum number of iterations for the algorithm. Default is 200. |
Details
'kdeem.h' can be used to estimate parameters in a mixture-of-regressions model with independent identically distributed errors. The model is defined as follows:
Here, ,
and
represents identical unspecified density functions.
The bandwidth of the kernel density estimation is calculated adaptively using the
bw.SJ
function from the ‘stats’
package, which implements the method of Sheather & Jones (1991) for bandwidth selection based on pilot estimation
of derivatives.
For the calculation of in the M-step,
this function employs the universal optimizer
ucminf
from the ‘ucminf’ package.
Value
A list containing the following elements:
posterior |
posterior probabilities of each observation belonging to each component. |
beta |
estimated regression coefficients. |
pi |
estimated mixing proportions. |
h |
bandwidth used for the kernel estimation. |
References
Hunter, D. R., & Young, D. S. (2012). Semiparametric mixtures of regressions. Journal of Nonparametric Statistics, 24(1), 19-38.
Ma, Y., Wang, S., Xu, L., & Yao, W. (2021). Semiparametric mixture regression with unspecified error distributions. Test, 30, 429-444.
See Also
kdeem
, kdeem.lse
, bw.SJ
for bandwidth calculation, and ucminf
for beta calculation.
Examples
# See examples for the `kdeem' function.