Questions tagged [mean-absolute-deviation]
Mean absolute deviation around the mean. Use [mad] for median absolute deviation around the median.
53 questions
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"The standard deviation is the statistical measure that describes, on average, how far each data point is from the mean"?
I have seen this sentence or similar statments many times:
The standard deviation is the statistical measure that describes, on
average, how far each data point is from the mean.
But I thought the ...
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OLS vs MLE when errors are not normally distributed (Laplace distributed)
We say that under assumptions of the Gauss-Markov theorem, OLS is BLUE. The Gauss-Markov theorem doesn't mention the normality of errors.
If the errors are distributed as per the Laplace distribution,...
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What makes the difference between the Mean Absolute Deviation (AAD) and Standard Deviation of a distrubution constant?
We can see very nicely in the normal distribution that the relationship between the mean absolute deviation and standard deviation is a constant ratio (by sqrt(2/pi)). What is it that gives a ...
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Are there cases where we need to avoid the usage of IQR?
Let's consider the interquartile range (IQR), the standard deviation (SD) and the mean absolute deviation (MAD). We know that "one of the most common robust measures of scale is the interquartile ...
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Upper bound on absolute difference with squares
I'm looking for an upper bound on $E_X\left[\left\vert X^2-(E[X])^2\right\vert\right]$, where $X$ is a nonnegative random variable, with known $E[X]$ and $E[X^2]$, but unknown higher moments.
A lower ...
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Absolute deviation from the mean using logarithms
I am calculating the absolute deviation from the mean of a strictly positive set $\{x_1, x_2, \ldots, x_n\}$ like:
$$\left| x_i - \bar X\right|$$
My analysis makes it appropriate to work in logs ...
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Mean absolute deviation (MAD) analogy to 68-95-99 rule
With MAD, 50% of all values fall within one absolute deviation. How many within two, and three?
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Count the fraction of trials for which the absolute deviation from the mean is larger than the standard deviation?
So, I have a data set containing 99 elements each with their own associated value. I have computed the standard deviation and the mean, but I am a little stumped with how exactly I should proceed with ...
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Standard Deviations of Detrended Data vs Original Data
I'am interested to know the opinion on this matter.
I have Data of a Financial Security. The goal is to view the Standard Deviations levels of the data to possibly see patterns of behavior of the ...
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Mean Absolute Deviation for AR(1) process
Is there closed-form solution for mean absolute deviation (MAD) for AR(1) process?
$X_t = c + \beta X_{t-1} + \epsilon_t $
$\epsilon_t \sim N(0,\sigma^{\epsilon})$
(Similar to the variance and the ...
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How do I calculate Correlation Coefficient using Mean Absolute Deviation?
I am trying to calculate Pearson's Correlation Coefficient using the product of the Mean Absolute Deviations (MADs) of my two lists as denominators instead of the Standard Deviations. Effectively, ...
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Why is there no improvement when training Xgboost with pseudo-Huber loss?
In this StackOverflow post I asked if there was something wrong with my syntax when training an XGboost model (in R) with the native pseudo-Huber loss ...
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For multivariate linear regression, what is the partial derivative for Mean Absolute Error?
What is the partial derivative for MAE for multivariate linear regression? I understand that for mean squared error (MSE) the partial derivative with respect to some $\theta_1$ would be $-\theta_1 \...
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What are the drawbacks of aggregating regression results if error decreases?
I am trying to predict Total National Sales in dollars for a major retailer. However, the data I'm using exists at the state level, and includes several features around specific brands and foot ...
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Ho do I determine the probability of price reversals using linear regression?
In the screenshot, you will see the daily prices of Nasdaq. Each candle has a High, Low, Open and Close price.
I have drawn a regression line with a 2 standard deviation channel on either side.
How ...
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Alternative error measure--maximize data to have residuals less than given threshold
I am looking for a method which finds a linear model (2 input variables, everything reasonably close enough to normally distributed), but with an alternative measure of error. Every error measure I ...
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How to derive this MAE error bound on the central limit theorem?
Is this derived from Chebyshev's inequality or a tail bound theorem? If not, how was it derived?
Does this require the existence of the third moment?
Does this bound suggest the normal approximation ...
user271077
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How to fix heteroscedasticity (funnel shape)?
I am running a mlr in python on a dataset with 2D feature vectors, X1 and X2 on a single response, Y. The data ends up being funnel-shaped, as below:
X1 v Y, with the colors being X2.
It was ...
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Compare variables with zeta-score
Assume the calculation of a physical quantity $x$ from a given formula i.e. $$x=\dfrac{a*b}{c}$$ where $a, b$ and $c$ are experimental observables, therefore $x$ is a quantity derived from ...
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Estimating Expected Order Statistics
I have a fairly basic question that I'm looking for a reference for.
First, a couple definitions. Let's say $X_1,\ldots,X_n$ are IID samples from a distribution $F$ over $[0,1]$. For any $k\in\{1,\...
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Rephrasing Statistics using MAD
I just got done reading Gorard's "Revisiting a 90-year-old debate: the advantages of the mean deviation." (https://www.leeds.ac.uk/educol/documents/00003759.htm) I'm no expert at statistics; in fact, ...
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Why does Mean deviation = Standard deviation = Range/2?
We know that mean deviation and standard deviation are two different things but why are both of them equal to Range/2?
Range ($R$) = Highest value - lowest value
Mean deviation ($\text{MD}$) = ...
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An efficient algorithm for sliding mean deviation
I'm searching for a computationally efficient algorithm to calculate the sliding mean deviation from sample $x_a$ to sample $x_b$ belonging to a large set $x_0, x_1 ... x_n$ with the condition that $a$...
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Is standard deviation always larger than mean deviation? [duplicate]
If yes why is it the case that it have this property? There must be some mathematical proof or intuitive understanding in that case.
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Is mean deviation the same as mean absolute difference?
Do both terms mean the same thing or are they different?
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