Questions tagged [mean-absolute-deviation]

Mean absolute deviation around the mean. Use [mad] for median absolute deviation around the median.

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15 views

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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Estimate the error bound of a histogram based mean absolute deviation approximation

Given a sequence of numbers $A = a_1, a_2, \cdots, a_n$. One way to calculate the mean absolute deviation of $A$ is by $G(A)= \sum_{i=0}^n |a_i - median(A)|$. yet, there can be an alternative, by ...
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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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What is the maximum entropy distribution given *conditional* means and MADs?

I know the maximum entropy distribution given the mean and MAD (Mean Absolute Difference) around the mean (it's the Laplace distribution, a proof here for example). I also know the maximum entropy ...
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A fair group allocation

Assume that I have 4 groups and 16 players that I wish to allocate among the groups. Each player has its own ranking (ELO or something). The group ranking is just the sum of rankings of players in ...
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57 views

How to calculate the running mean absolute deviation

I wish to calculate the running mean absolute deviation (MAD) without storing the previous n data points. This calculation is for a continuous stream of data, i.e. infinite length. I am trying to ...
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53 views

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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215 views

an upper bound of mean absolute difference?

Let $X$ be an integrable random variable with CDF $F$ and inverse CDF $F^*$. $Y$ is iid with $X$. Prove $$E|X-Y| \leq \frac{2}{\sqrt{3}}\sigma,$$ where $\sigma=\sqrt{Var(X)} = \sqrt{E[(X-\mu)^2]}$. I ...
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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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25 views

Why isn't absolute deviation used [duplicate]

If the reason that standard deviation is used is that it's easier to just square the distance every time than find the absolute value. Then why is √(E(x-m)^2)/n not used because if I'm not mistaken |x|...
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34 views

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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We square at the variance and SD is it due a link with to Gaussian function? [duplicate]

I had almost same question as "Why square the difference instead of taking the absolute value in standard deviation?". But I also noticed the $\sigma$ or population standard deviation is ...
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1answer
13 views

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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103 views

Random variables $(X,Y)$ with $\text{Var}(X)<\text{Var}(Y)$ and $\mathbb{E}(|X-\mu_X|)>\mathbb{E}(|Y-\mu_Y|)$

I am looking for an example of a pair of random variables $(X,Y)$ with expected values $(\mu_X,\mu_Y)$ satisfying the following relationships: $$ \text{Var}(X)<\text{Var}(Y) $$ and $$ \mathbb{E}(|X-...
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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 ...
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how to detect a 5% deviation between more than 2 numbers

Dear StackExchange Team in the industry there are GAs generators that have hundreds of instrument measuring process values, such as pressure, temperatures, etc. we have a simple case where a ...
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Estimate MAD of marginal means

Assume we have a (unknown) random variable $X(r,p)$ over the space $R \times P$. From this distribution we have observations $X(r_j, p^j_i)$. For every $j$ there are on average around 60 $i$'s lets ...
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Considering the reliability of results given they were produced using different amounts of data

I am doing some deep learning and I have two lists of numbers: the predictions from a regression neural network and the ...
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1answer
151 views

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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216 views

Is mean absolute deviation smaller than standard deviation for $n\ge 3$?

I want to compare the mean absolute deviation with standard deviation in general case with this definition: $$MAD = \frac{1}{n-1}\sum_1^n|x_i - \mu|, \qquad SD = \sqrt{\frac{\sum_1^n(x_i-\mu)^2}{n-1}}...
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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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1answer
268 views

Why do we use squared deviations to compute the SD, given that it amplifies the effect of outliers? [duplicate]

Suppose I have the following hypothetical data: One thousand times value 15 (i.e., 15 occurs 1000 times) and a single outlier value - 115 (i.e., 115 occurs just once - an outlier) Thus the mean is: $...
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297 views

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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159 views

Statistical test for comparing the performance of two methods using absolute differences

I am doing a study where I have to compare tumor sizes measured using two different methods with the real tumor size. What I want to prove is that the absolute difference between method 1 and real ...
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2answers
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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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132 views

Verbal Description Of The RSE

I'm reading An Introduction to Statistical Learning, currently on page 69, the chapter on Simple Linear Regression. The text says: In the case of the advertising data, we see from the linear ...
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1k views

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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3k views

Why not use modulus for variance? [duplicate]

I am trying to wrap my mind around the variance definition. Given a set of values S and n = #(S), the variance is defined as: $$ \operatorname{var}(S) = \frac{\sum_{i=1}^n( S_i - \operatorname{mean}(...
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127 views

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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1answer
560 views

Best way to describe changes in performance through time.

I'm wondering how to explain changes in production/performance metrics quarter to quarter. In the example below, one can see that the average processing time for "widgets" has decreased substantially ...
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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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1answer
407 views

Why don't dispersions like median deviation and mode deviation exists on the lines of mean deviation?

Or to say in the formula MD=$\frac{1}{N}\sum_{i=1}^{N}|x_i-\overline{x}|$ why can't we have median or mode instead of mean($\overline{x}$) and as a result speak about additional possible measures of ...
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1k views

Is mean deviation the same as mean absolute difference?

Do both terms mean the same thing or are they different?
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1answer
49 views

Variance of Binomial total deviation

I have a Binomial random variable $X \sim B(n,p)$. Is there a closed form expression or an upper bound for the variance of the absolute deviation $|X-\mathbb{E}[X]|$ ?
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765 views

Mean Absolute Deviation of Student t distributions?

I could only find these two formulae, both apparently with some issues. Which is the correct one? Online references and derivation would be especially appreciated.
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Relative Mean Deviation [closed]

The Mean Deviation, also referred to as Absolute Average Deviation, is sometimes preferred to the Standard Deviation (Cf. Gorard 2004). For a sample, it can be expressed as: $MD = \frac{1}{n} \sum\...
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301 views

Difference between absolute deviation to population median and sample mean

I have independent variables $X_i\in[0;1]$ and suppose they are uniformly distributed. If you want to minimize the total absolute deviation to a fixed number, how much can you gain from using the ...