R package KoulMde: Koul’s Minimum Distance Estimation in Linear Regression and Autoregression Model. 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 proposed a nonparametric minimum distance estimation method by minimizing L2-type distance between certain weighted residual empirical distribution functions. He also proposed a simpler version of the loss function by using symmetry of the integrating measure in the distance. This package contains three functions: KoulLrMde(), KoulArMde(), and Koul2StageMde(). KoulLrMde() and KoulArMde() 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.

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  1. Jiwoong Kim: A Fast Algorithm for the Coordinate-wise Minimum Distance Estimation (2017) arXiv