kdeem.lse | R Documentation |
‘kdeem.lse’ is used for semiparametric mixture regression based on least squares estimation (Hunter and Young, 2012) using a kernel density-based expectation-maximization (EM)-type algorithm with unspecified homogeneous error distributions.
kdeem.lse(x, y, C = 2, ini = NULL)
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. As of version 1.1.0, C must be set to 2. |
ini |
initial values for the parameters. Default is NULL, which obtains the initial values
using the |
As of version 1.1.0, this function can only be used for a two-component mixture-of-regressions model
with independent identically distributed errors. Assuming C=2
, the model is defined as follows:
f_{Y|\boldsymbol{X}}(y,\boldsymbol{x},\boldsymbol{\theta},g) = \sum_{j=1}^C\pi_jg(y-\boldsymbol{x}^{\top}\boldsymbol{\beta}_j).
Here, \boldsymbol{\theta}=(\pi_1,...,\pi_{C-1},\boldsymbol{\beta}_1^{\top},\cdots,\boldsymbol{\beta}_C^{\top})
,
and g(\cdot)
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. This function employs weighted least square estimation for \beta
in the M-step (Hunter and Young, 2012),
where the weight is the posterior probability of an observation belonging to each component.
A list containing the following elements:
posterior |
posterior probabilities of each observation belonging to each component. |
beta |
estimated regression coefficients. |
tau |
estimated precision parameter, the inverse of standard deviation. |
pi |
estimated mixing proportions. |
h |
bandwidth used for the kernel estimation. |
Hunter, D. R., and Young, D. S. (2012). Semiparametric mixtures of regressions. Journal of Nonparametric Statistics, 24(1), 19-38.
Ma, Y., Wang, S., Xu, L., and Yao, W. (2021). Semiparametric mixture regression with unspecified error distributions. Test, 30, 429-444.
kdeem
, kdeem.h
, bw.SJ
for bandwidth calculation, and regmixEM
for initial value calculation.
# See examples for the `kdeem' function.
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