Median Absolute Deviation (MAD) is a measure of variability in a sample of data, and is often used as an alternative to measures like standard deviation since it is more resistant to outliers.

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Are there non-trivial settings where the MAD statistic has a closed-form density?

The MAD statistic of an iid sample $(x_1,\ldots,x_n)$ is defined as the median of the absolute deviation from the median: $$ ...
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MAD formula for outlier detection

Does anyone know what is the name of this formula? $$M_i = \displaystyle\frac{0.6745(x_i - \hat{x})}{\mathrm{MAD}}$$ where $\textrm{MAD}$ is the median absolute deviation and $\hat{x}$ is the median ...
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Better than Mad, Derive $Q_n$

Could someone be so kind as to walk me through how to do this equation on a dataset? on pg 5 (marked as 1277) equation 3.3 of this paper. $$Q_n = c|x_i-x_j|_{(k)},\;\;1\leq i<j\leq ...
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Bar plot with median +/- median absolute deviation in scientific publication

I know bar plots usually represents mean +/- sem, but if the data is non-normal, is it ok to bar plot median +/- mad? I don't like box plots. Suggestison?
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Proving the consistancy of the MAD

I am trying to prove that the median absolute deviation from the median (MAD), with k=1.4862, is a consistent estimator of the standard deviation.
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Alternatives to MAD to find a yardstick to assess data

In a paper by Rousseeuw and Croux from 1993 ("Alternatives to the Median Absolute deviation", page 1274, link to pdf), I came across an indicator I'm considering using. The formula is: $$ Sn = C\, ...
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131 views

What distribution has the maximum entropy for a known mean absolute deviation?

I was reading the discussion on Hacker News about the use of the standard deviation as opposed to other metrics such as the mean absolute deviation. So, if we were to follow the principle of maximum ...
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94 views

Understanding MAD Results

I'm using R to calculate the median absolute deviation for a few distributions, but some of the values I'm calculating do not seem realistic at all. I have the following distribution: ...
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275 views

MAD in relation to 95% confidence

MAD (Median Absolute Deviation) is: $\text{MAD} = M_i(|x_i-M_j(x_j)|)$ where $M()$ is the median operator ($M_i(x_i) = \text{median}(x_1,...,x_n)$). I'd like to scale the MAD in such a way as to ...
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402 views

Does a median-unbiased estimator minimize mean absolute deviance?

This is a follow-up but also a different question of my previous one. I read on Wikipedia that "A median-unbiased estimator minimizes the risk with respect to the absolute-deviation loss function, as ...
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451 views

Median + MAD for skewed data

I am trying to figure out what happens if you apply Hampel's outlier detection technique based on the median and the MAD to data that is skewed. Apparently, the advantage of Hampel's method over ...
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214 views

Propagation of errors with median absolute deviation from the median?

Is there a theoretically-sound way to perform propagation of errors with robust statistics? I am trying to characterize the errors inherent in a measurement and propagate the uncertainty through ...
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Outlier detection for heavy-tailed data

Applying modified z-score for outlier elimination on some data (Iglewicz and Hoaglin, 1993), I discovered that a big proportion of the data (~10%) was outside the range ...
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Using MAD as a way of defining a threshold for significance testing

If I have a set of terms each term having a particular frequency associated with it (the number of the times the term has appeared in fixed corpus of papers), then is the following method of ...
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731 views

MAD equivalent for standard error

As far as I know, one can calculate the relative standard error from the standard deviation of a data sample. I am looking for the Median Absolute Deviation equivalent for standard error. Does one ...
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Mean$\pm$SD or Median$\pm$MAD to summarise a highly skewed variable?

I'm working on highly skewed data, so I'm using the median instead of the mean to summarise the central tendency. I'd like to have a measure of dispersion While I often see people reporting mean ...
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Use of robust spread measures such median average deviation and median filters for time series

I have a time series where I need to detect gross anomalies due to coding errors, not small shifts in the structure of the series. I am interested in the most recent data points, not historical data ...
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How to calculate overall standard deviation from standard deviation of sub-periods?

If I have the mean, s.d., median and count for sample A, and the same for sample B, can I throw away the samples, and calculate exactly mean, median and s.d. for the combination? Well the mean is ...
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Median of medians as robust mean of means?

The location and scale of a normally distributed data can be estimated by sampling the data then taking the mean of the sample means and standard deviations, respectively. For non-normal ...