English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The ordinary least squares and ridge regression estimators in a multiple linear regression model with multicollinearity and  y -direction outliers lead to unfavorable results. In order to mitigate such situation, the available literature provides few ridge M-estimators to get precise estimates. The ridge parameter,  k , plays a vital role in a bias-variance tradeoff for these estimators. However, for high signal-to-noise ratio and multicollinearity with  y -direction outliers, the available methods may not perform well in terms of their mean squared error. In this article, we propose a new quantile based ridge M-estimator. The new estimator gives an automated choice of quantile probability of ridge parameter according to the level of noise and multicollinearity. Based on a simulation study, the new estimator outperforms the ordinary least square estimator, ridge estimator, and other considered ridge M-estimators especially for high multicollinearity, significant error variance, and  y -direction outliers. Besides normal distribution, new estimator also performs well for heavy-tailed error distribution. Finally, two real-life examples are used to illustrate the application of the proposed estimator.

New quantile based ridge M-estimator for linear regression models with multicollinearity and outliers