Robust mediation analysis based on median regression.

Robust PLS regression based on simple least median squares regression

Exploratory Study on Median-based Robust Regression Methods for Linear Calibration in Atomic Absorption Spectrometric Analysis

A suitable strategy has been developed either to avoid the influence of outliers or to reject them in the case of homoscedasticity in routine analysis. Several robust methods based on the median, namely the single median, the repeated median and the least median of squares, are introduced and evaluated. These methods were used for the analysis of real data obtained from atomic absorption spectr...

Robust Regression by Boosting the Median

Most boosting regression algorithms use the weighted average of base regressors as their final regressor. In this paper we analyze the choice of the weighted median. We propose a general boosting algorithm based on this approach. We prove boosting-type convergence of the algorithm and give clear conditions for the convergence of the robust training error. The algorithm recovers ADABOOST and ADA...

Robust Nonparametric Estimation via Wavelet Median Regression

In this paper we develop a nonparametric regression method that is simultaneously adaptive over a wide range of function classes for the regression function and robust over a large collection of error distributions, including those that are heavy-tailed, and may not even possess variances or means. Our approach is to first use local medians to turn the problem of nonparametric regression with u...

Testing Mediation with Regression Analysis

The purpose of Steps 1-3 is to establish that zero-order relationships among the variables exist. If one or more of these relationships are nonsignificant, researchers usually conclude that mediation is not possible or likely (although this is not always true; see MacKinnon, Fairchild, & Fritz, 2007). Assuming there are significant relationships from Steps 1 through 3, one proceeds to Step 4. I...