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Mean Absolute Error Gaussian

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Pham-Gia Some applications of the Lorenz curve in decision analysis Amer. Pearson Methods of estimating from samples the population standard deviation Journ. In it, you'll get: The week's top questions and answers Important community announcements Questions that need answers see an example newsletter Linked 0 Whats the background of the mean squared error? A truly fundamental reason that has not been invoked in any answer yet is the unique role played by the variance in the Central Limit Theorem. this content

The sd is not always the best statistic. –RockScience Nov 25 '10 at 3:03 1 Great counter-example as to when the standard deviation is not the best way to think Sometimes you want your error to be in the same units as your data. Using the linearly proportional penalty function, the regression will assign less weight to outliers than when using the squared proportional penalty function. Rogers, J.W. https://en.wikipedia.org/wiki/Average_absolute_deviation

Mean Absolute Deviation Formula

If taking derivatives is not involved, calculating absolute error is as easy as calculating squared error, then why squared error is so prevalent? not too close to a "boundary"), we can taylor expand the log probability about its maximum $\theta_\max$. Bloomfield, W.S.

It's not a far jump to see how this happens still even without the data being almost all 1's and 3'd. Example: squares can be integrated, differentiated, can be used in trigonometric, logarithmic and other functions, with ease. more stack exchange communities company blog Stack Exchange Inbox Reputation and Badges sign up log in tour help Tour Start here for a quick overview of the site Help Center Detailed Average Deviation Vs Standard Deviation I work with large data sets, and CPU time is important.

However in-sample measurements deliver values of the ratio of mean average deviation / standard deviation for a given Gaussian sample n with the following bounds: w n ∈ [ 0 , Mean Absolute Deviation Vs Standard Deviation However, this argument is based on the notion of mean-unbiasedness. Oh well. ;-) –Sabuncu Feb 11 '14 at 21:55 | show 14 more comments 20 Answers 20 active oldest votes up vote 115 down vote accepted If the goal of the http://www.sciencedirect.com/science/article/pii/S0895717701001091 In cases where you want to emphasize the spread of your errors, basically you want to penalize the errors that are farther away from the mean (usually 0 in machine learning,

MSE has nice mathematical properties which makes it easier to compute the gradient. Relative Deviation As an example, you can take a look at Matlab's robustfit function which allows you to choose a different penalty (also called 'weight') function for your regression. Even for non-normal distributions it can be helpful to think in a normal framework. One more time:If the estimate is 2, sum of absolute errors is: (2-0)*50 + (100-2)*50 = 100*50 = 5,000If the estimate is 50, sum of absolute errors is: (50-0)*50 + (100-50)*50

Mean Absolute Deviation Vs Standard Deviation

As also explained in the wikipedia entry, the choice of the loss functions depends on how do you value deviations from your targeted object. click site I used to feel strongly that the use of L2 is unfounded. Mean Absolute Deviation Formula Would you like to answer one of these unanswered questions instead? Average Deviation Formula But if none of the above definitions of loss fit your problem at hand, because e.g.

Which in most of the case average of sum of the error difference but its always recommended to use Squared average.Is there any releavant fact that supports it ?UpdateCancelAnswer Wiki5 Answers http://threadspodcast.com/mean-absolute/mean-absolute-relative-error.html Lippmann, car les expérimentateurs s'imaginent que c'est un théorème de mathématiques, et les mathématiciens que c'est un fait expérimental. "Everyone is sure of this [that errors are normally distributed], Mr. Sorry, unclear before. Now imagine that the data are 2.5, 1, 3, 1, 3, etc. Median Absolute Deviation

Menu Log in or Sign up Contact Us Help About Top Terms and Rules Privacy Policy © 2001-2016 Physics Forums This page may be out of date. Q.2 is challenging. But aren't there also direct physics applications for the Gaussian distribution? have a peek at these guys The SD is surprisingly difficult to interpret to non-statisticians.

If all deviations are equally bad for you no matter their sign, then you could use the absolute loss function. Relative Average Deviation Quantile regression and its multiple variante is an example of that. –robin girard Jul 24 '10 at 6:01 11 Yes, but finding the actual number you want, rather than just Which means that the cost of the lobster errors isn't $100,000 -- it's only $80,000.

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This accords well with what many think is an appropriate way of doing things. –Dilip Sarwate Apr 18 '15 at 3:19 add a comment| 5 Answers 5 active oldest votes up For the normal distribution, the ratio of mean absolute deviation to standard deviation is 2 / π = 0.79788456 … {\displaystyle {\sqrt {2/\pi }}=0.79788456\ldots } . The notions of projection and perpendicular etc, depends on the metric. Mean Absolute Deviation Excel A statistician comes along, and analyzes her estimates over the past 1000 days.

That's an absolute error of \$500. The possible advantages of the mean absolute deviation ‘effect’ size, Social Research Update, 65:1. Why? check my blog Median does not require sorting. –Neil G May 19 '14 at 20:02 | show 3 more comments up vote 63 down vote One way you can think of this is that

Boos, Hughes-Oliver Applications of Basu's theorem The American Statistician, 52 (3) (1998), pp. 218–221 21 E.M. Rao, Y.Q. Having a square as opposed to the absolute value function gives a nice continuous and differentiable function (absolute value is not differentiable at 0) - which makes it the natural choice, Nobody there will square the errors; the differences are the point.

Find first non-repetitive char in a string Gender roles for a jungle treehouse culture Spaced-out numbers Why did Fudge and the Weasleys come to the Leaky Cauldron in the PoA? I suppose you could say that absolute difference assigns equal weight to the spread of data where as squaring emphasises the extremes.