Abstract
The stochastic restrictedr-kclass estimator and stochastic restrictedr-dclass estimator are proposed for the vector of parameters in a multiple linear regression model with stochastic linear restrictions. The mean squared error matrix of the proposed estimators is derived and compared, and some properties of the proposed estimators are also discussed. Finally, a numerical example is given to show some of the theoretical results.
Highlights
The problem of multicollinearity or the ill-conditioned design matrix in linear regression model is very well known in statistics
An alternative method to deal with multicollinearity problem is to consider parameter estimation with some restrictions on the unknown parameters, which may be exact or stochastic restrictions [8]
In order to overcome multicollinearity, we introduce a stochastic restricted r-k class estimator and a stochastic restricted r-d class estimator for the vector of parameters in a linear regression model when additional stochastic linear restrictions are assumed to hold
Summary
The problem of multicollinearity or the ill-conditioned design matrix in linear regression model is very well known in statistics. An alternative method to deal with multicollinearity problem is to consider parameter estimation with some restrictions on the unknown parameters, which may be exact or stochastic restrictions [8]. When stochastic additional restrictions on the parameter vector are supposed to hold, Durbin [9], Theil and Goldberger [10], and Theil [11] proposed the ordinary mixed estimator (OME). In order to overcome multicollinearity, we introduce a stochastic restricted r-k class estimator and a stochastic restricted r-d class estimator for the vector of parameters in a linear regression model when additional stochastic linear restrictions are assumed to hold.
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