Stochastic and Deterministic Study of Ridge Regression

نوع المستند : المقالة الأصلية

المؤلف

Noha E. Abd Al-Rahman1, Salwa A. Mousa2 and Amina E. Abo-Hussien3 1 Department of Statistics, Faculty of Commerce, Al-Azhar University, Girls' Branch, Dakahlia , Egypt.

المستخلص

The present paper is concerned with studying the ridge parameters  through deterministic and stochastic approach in the case of ordinary ridge regression (ORR). In the deterministic approach, some new formulas for the ridge parameters are proposed and compared with the formula suggested by Hoerl and Kennard (1970a). The performance of the proposed ridge parameters is evaluated through a simulation study in the presence of multicollinearity. An application using real data is given. The evaluation is based on the mean square error (MSE) and relative MSE (RMSE). In the stochastic approach, the main properties of the proposed new formulas and the formula suggested by Hoerl and Kennard (1970a) are studied. The probability density function (pdf) and distribution function of the formulas are derived. The empirical distributions of these formulas are derived using Pearson’s method. It is found that the performance of the new formulas are better than ordinary least squares (OLS) and the formula suggested by Hoerl and Kennard (1970 a) for all selected distributions.  

نقاط رئيسية

Ridge Regression;

Deterministic approach;

Stochastic approach;

Monte Carlo simulation; 

Mean square error; Relative mean square error; Sampling distribution.  

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