# Koul's Minimum Distance Estimation in Linear Regression and
Autoregression Model by Coordinate Descent Algorithm

Consider linear regression model and autoregressive model of
order q where errors in the linear regression model and innovations in the
autoregression model are independent and symmetrically distributed. Hira L. Koul
(1986) proposed a nonparametric minimum distance
estimation method by minimizing L2-type distance between certain weighted
residual empirical processes. He also proposed a simpler version of the loss
function by using symmetry of the integrating measure in the distance. Kim
(2018) proposed a fast computational method
which enables practitioners to compute the minimum distance estimator of the vector
of general multiple regression parameters for several integrating measures. This
package contains three functions: KoulLrMde(), KoulArMde(), and Koul2StageMde().
The former two provide minimum distance estimators for linear regression model
and autoregression model, respectively, where both are based on Koul's method.
These two functions take much less time for the computation than those based
on parametric minimum distance estimation methods. Koul2StageMde() provides
estimators for regression and autoregressive coefficients of linear regression
model with autoregressive errors through minimum distant method of two stages.
The new version is written in Rcpp and dramatically reduces computational time.