Alternatives to the Median Absolute Deviation

Bahadur Representations for the Median Absolute Deviation and Its Modifications

The median absolute deviation about the median (MAD) is an important univariate spread measure having wide appeal due to its highly robust sample version. A powerful tool in treating the asymptotics of a statistic is a linearization, i.e., a Bahadur representation. Here we establish both strong and weak Bahadur representations for the sample MAD. The strong version is the first in the literatur...

Detecting outliers: Do not use standard deviation around the mean, use absolute deviation around the median

MULTIPERIOD CREDIBILITIC MEAN SEMI-ABSOLUTE DEVIATION PORTFOLIO SELECTION

In this paper, we discuss a multiperiod portfolio selection problem with fuzzy returns. We present a new credibilitic multiperiod mean semi- absolute deviation portfolio selection with some real factors including transaction costs, borrowing constraints, entropy constraints, threshold constraints and risk control. In the proposed model, we quantify the investment return and risk associated with...

Analysis of least absolute deviation

The least absolute deviation or L1 method is a widely known alternative to the classical least squares or L2 method for statistical analysis of linear regression models. Instead of minimizing the sum of squared errors, it minimizes the sum of absolute values of errors. Despite its long history and many ground-breaking works (cf. Portnoy and Koenker (1997) and references therein), the former has...

MEAN-ABSOLUTE DEVIATION PORTFOLIO SELECTION MODEL WITH FUZZY RETURNS

In this paper, we consider portfolio selection problem in which security returns are regarded as fuzzy variables rather than random variables. We first introduce a concept of absolute deviation for fuzzy variables and prove some useful properties, which imply that absolute deviation may be used to measure risk well. Then we propose two mean-absolute deviation models by defining risk as abs...