Resampling method for the data adaptive choice of tuning constant in robust regression

Robust regression estimators are designed to easily fit the data sets that are contaminated with outliers. a common problem associated with robust regression estimators to be completely specified is the proper choice of cut-off points called tuning constant. the choice of the tuning constant is somewhat arbitrary and is largely the matter of the personal preference. several authors suggested different value of tuning constant ‘c’ for various m estimators. yohai (1974) considered a class of error distribution in the linear regression model and showed how to choose c for huber’s robust regression estimator so that the resulting estimator was minimax over the class of error distribution. kelly(1992),with a different approach,showed that the choice of tuning constant is critical in the trade-off between bias and variance and suggested minimum choice of jackknife asymptotic mean-square error of the estimator to choose tuning constant. salahuddin (1990) used leave-one-out cross-validation to choose an optimal value of tuning constant for andrews’ wave estimator. we propose k-fold crossvalidation procedure for choosing optimal choice of tuning constant to minimize crossvalidated absolute median predicted residual. furthermore,we investigated a suitable preliminary resistant estimator to arrive at a good robust fit. andrew’s,tukey’s,qadir and asad robust regression estimators are explored and compared. the study found that the proposed technique is working well. © 2015 pakistan journal of statistics.