Mean Squared Error Comparisons of Some Biased Regression Estimators

Combining the Liu Estimator and the Principal Component Regression Estimator

“…We illustrate our findings in Theorem 3 with a numerical example based on the widely-analyzed dataset on Portland cement (see, for example, (7,8,12)). We illustrate our findings in Theorem 3 with a numerical example based on the widely-analyzed dataset on Portland cement (see, for example, (7,8,12)).…”

A Prediction-Oriented Criterion for Choosing the Biasing Parameter in Liu Estimation

“…The estimatorˆ d is called the Liu estimator by Akdeniz and Kaçıranlar (1995) and Gruber (1998). Since then, the properties ofˆ d have been studied by Kaçıranlar (1995, 2001), Kaçıranlar et al (1999), and Sakallıoglu et al (2001), to mention a few. The advantage ofˆ d overˆ k is thatˆ d is a linear function of d. So the selection of d is simpler than the selection of k.…”

The Research on Two Kinds of Restricted Biased Estimators Based on Mean Squared Error Matrix

“…Obviously, the comparison among biased estimators is of a certain significance in the aspects of theory and practice. Statistics have compared some biased estimators without additional linear equation restrictions, for example, Sakallıoglu et al (2001) dealt with the comparisons among ridge estimator, Liu estimator, and iteration estimator constructed as alternatives to the least squares estimator when multicollinearity is present. Akdeniz and Erol (2003) compared the (almost unbiased) generalized ridge regression estimator with the (almost unbiased) generalized Liu estimator in the matrix mean squared error sense.…”

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Sakallıoglu et al (2001) dealt with the comparisons among the ridge estimator, Liu estimator, and iteration estimator. Akdeniz and Erol (2003) have compared the (almost unbiased) generalized ridge regression estimator with the (almost unbiased) generalized Liu estimator in the matrix mean squared error sense.

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