Robustness in general refers to a statistic's insensitivity to deviations from its underlying assumptions (Huber and Ronchetti, 2009).

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Assumption about Systematic Errors

In Maronna, Martin and Yohai's Robust Statistics (2006, p.17), they describe a location model as follows. $$x_i = \mu + u_i,$$ where $x_i$ is the $i$th observation; $\mu$ is the hypothetical mean ...
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20 views

Higher order robust moments

Is it possible to calculate the 5th, 6th, 7th, 8th and higher-order central robust moments? Is there any other methodology and implementation? How are these comparable to regular sample moments?
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22 views

What is robust data?

This is the rather confusing go-to internet definition for robust data: Robust data is data that is constructed to survive and function in multiple settings. It's reusable. It can be updated. Anyone ...
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22 views

Trying to Find Article by Tukey

I am trying to find a commonly cited paper by John Tukey published in 1960 called "A survey of sampling from contaminated distributions", from a monograph(?) called "Contributions in Probability and ...
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5 views

Finding an area of low variance for (robust) linear regression

In order to determine a function for a Good-Turing approximation of the number $N_r$ of distinct words that occur $r$ times in a hypothetical language corpus, I'd like to run a (log-)linear regression ...
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1answer
79 views

Robust estimates of the covariance matrix in the big data space

I am trying to compute the robust estimates of the covariance matrix (and also the mean) in the big data space. I am aware of FastMVE and FastMCD (Minimum Covariance Determinant and Minimum Volume ...
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1answer
124 views

How to find set of directions in Stahel-Donoho outlyingness measure?

Currently I’m trying to understand and use the Stahel-Donoho outlyngness measure. But unfortunately I’ve got a problem in the part where one is taking the maximum over the set of directions. I found ...
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1answer
51 views

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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1answer
68 views

How to efficiently compute Theil-Sen estimator?

The Theil-Sen estimator is of interest to me, however when I implement it myself I end up with something that scales as O(n^2). According to wikipedia, it can be calculated exactly in O(n log(n)). Can ...
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42 views

Two-way between groups ANOVA for non-normal data

I'm doing a study on visual selective attention (VSA) and how this is influenced by gender and video gaming. So my dependent variable is VSA (continuous) and my two independent variables are gender ...
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76 views

Robust regression in R

I've used an ordinary least square linear regression model in R that looks something like this: ols <- lm(DV ~ IV1 + IV2) When I type this: ...
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1answer
64 views

Is the linear probability model generalisable to ordered logit/probit regressions?

I have a set of data where the dependent variable is an ordered response with 7 levels and I've fitted an ordered logit model to the data, and now I want to conduct some robustness checks on the ...
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16 views

Online moving median [duplicate]

So I can use "EWMA" (1) to update an estimate of the mean as each new measurement is received. If I know the window size of the smooth($\eta$), the previous estimate($ \bar{x}_t$), and the new ...
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23 views

Regression excercise

I have been sitting with this regression problem for about four months and can not seem to figure it out. My data show signs of heteroscedasticity and i tried many types of transformations with no ...
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2answers
241 views

Outliers and the mean

I would like to know what the following example is called in mathematics: In a gymnastics competition the judges scored a competitor as 10, 8, 3, 7, 7, 9, and 8. I recall that the ending score was ...
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1answer
119 views

What location parameter is modelled by robust regression?

There is quite some number of ways how to robustly fit a linear regression model, e.g. using M-estimation based on Tukey's biweight loss or on Huber's loss, see e.g. Wikipedia. I got two questions ...
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13 views

What are the canonical data sets used for testing robust linear fitting?

The UCI database (link) is one of the repositories for canonical data. It has ~295 data sets for use. There are many others. (link) While data can be useful not all data is relevant for all ...
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4answers
772 views

Good form to remove outliers?

I'm working on statistics for software builds. I have data for each build on pass/fail and elapsed time and we generate ~200 of these/week. The success rate is easy to aggregate, I can say that 45% ...
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1answer
30 views

Adjust standard errors for within correlation

I am trying to replicate a table and in one of the notes it's written that 'standard errors are adjusted to account for the within-analyst correlation of the observations' I am running my regressions ...
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1answer
91 views

Why are Winsorized random variables independent?

While studying trimmed mean I understood that if I have some random variables $X_1, X_2, .., X_n$ by ordering them and trimming, the variables are no longer independent. However it is said that "by ...
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124 views

Comparison between MAD and SD

I am reading Huber's Robust Statistics (2nd). On page 2 and 3 he gave an example. The basic facts are summarized here. Let $(X_n)$ be a sequence of random variables and define two measures of spread ...
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101 views

Unbalanced Panel: pooled OLS vs FE vs RE - which method yield unbiased and robust estimators?

I am conducting an empirical study (relation between earnings and returns). I have an unbalanced panel with $N=449$ firms and $T=36$ time periods. Regarding the estimation methods I am confused: In ...
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48 views

Robust estimation in SPSS generalized mixed models

I'm using mixed models in SPSS 19 to analyse dietary data. The mixed procedure is used because we have more than one measurement from many of the participants. My problem is that many of my dependent ...
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39 views

R - Robust Ancova: Documentation/Examples for the ancmg function in the WRS package

Could anyone point me to a documentation or even better an example for the ancmg1 or ancmg functions of the WRS-package. There is a very short paragraph in the Wilcox' book about Robust Estimation, ...
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2answers
54 views

Obtaining error bars for a difference

I have a pair of data sets, and I want to know whether the medians of these two sets differ significantly. I've calculated the median of each set and subtracted them from each other. How can I ...
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2answers
77 views

Log-likelihood (and AIC) of robust nlrob model differs from standard nls model

Comparing models generated by nlrob to ones generated by nls, I've noticed that even though the models might be nearly identical, the log-likelihood of the models is sometimes significantly different, ...
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275 views

linear regression using heteroskedasticity robust standard errors in R

I want to perform an OLS regression on time series data using heteroskedasticity robust standard erros. So far i can come up with this: ...
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57 views

Methods to determine reliability of measurements using median and median absolute deviation

I have several datasets containing hundreds of variables, measured at the same time point and with the same method. Some of these variables have been measured more often and assume consistent values. ...
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74 views

Estimating means of correlated distributions with long tails

Suppose I have a relatively large number of samples (~1k) drawn from a series (~40) of increasingly long-tailed distributions (going from approximately normal to approximately log-normal). I want to ...
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204 views

Robust estimation of kurtosis?

I am using the usual estimator for kurtosis, $\hat{K}=\frac{\hat{\mu}_4}{\hat{\sigma}^4}$, but I notice that even small 'outliers' in my empirical distribution, i.e. small peaks far from the center, ...
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41 views

Delete observations for regression modelling

I am implementing robust regression on some data and when i tested the accuracy on a hold set of data, the accuracy was very bad. I have about 500 000 observations for the regression model and i ...
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21 views

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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2answers
61 views

How to test the robustness and the performance of a novel classification algorithm

Suppose you have a new algorithm that you want to publish. Are there any best practices and methodologies you usually consider in order to test the robustness and performance of a new method? The ...
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43 views

How robust is estimation using sum of powers? [closed]

Minimizing sum of squares for scale and location estimation is optimum wrt efficiency for normal distributions, and doing so but using the sum of absolute values is maximum likelihood estimation ...
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1answer
126 views

What makes an econometric model robust?

I was reading a paper on robustness (http://econ.ucsb.edu/~doug/245a/Papers/Robustness%20Checks.pdf) and they say: "To determine whether one has estimated effects of interest, $\beta$; or only ...
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50 views

Error message with robust regression in R

Whenever I run a robust regression model in R with rlm and with either M or MM methods, I get the following error message: Error: 'lqs' failed: all the samples ...
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1answer
117 views

Theil-Sen estimation

Is the theil-sen estimation in robust regression only limited to a two dimensional problem or can you use it for more than one indepedent variable as well?
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52 views

Robust estimator of mean for skewed data

For heavy-tailed symmetric data, a trimmed mean or other robust estimator of the mean could be a better estimator of the mean than the sample mean. The trimmed mean will be biased for a skewed ...
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1answer
89 views

Effective sample size of weighted regression

I am doing a basic linear regression with one predictor with some weighting in R, e.g.,: lm(response~explanatory, weights=w, data=mydata) The weights are ...
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1answer
223 views

Robust OLS verus ML with sandwich estimator

If you compare the standard errors of the OLS coefficients with the White correction, versus the ML estimates with the variance estimated with the sandwich estimator, which standard errors do you ...
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2answers
119 views

Robust regression - a better understanding

I looked at robust regression for the first time today and I am a bit confused, comparing it to something like ordinary least squares and I am not sure if I am on the right track. I read a few ...
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22 views

Robust variance estimators

Given $N$ data points in $\mathbb{R}^p$ - some of which are outliers (drawn from a different distribution from the inliers) - what sorts of algorithms have been designed to estimate the robust ...
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19 views

How should I choose WLS weights with categorical IVs?

I have a 2X2 design (2 categorical independent variables (IVs) with 2 levels each), and a single dependent variable (DV). I have 91 samples in total with these cell counts: 30, 19. 20, 22. My data for ...
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103 views

Robust regression goodness of fit

I'm using R to compute robust multiple linear regression. I use the command rlm from the package MASS. As psi function I use ...
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1answer
755 views

What is the minimum viable cell size for 2x2 ANOVA?

I have a 2x2, between-subjects experimental design (2 independent variables (IVs) with 2 levels each) and one dependent variable (DV). My data are unbalanced and an interaction between the IVs seems ...
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143 views

Differences between robustness checks and sensitivity analysis

This is a bit of a terminology question, but what is the difference between a robustness check and a sensitivity analysis? For example, if performing analysis to see how sensitive (or robust) a ...
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Is there a generalization of trimean to $n$-th order (central) moments?

I think trimean is the cat's meow. Is there a generalization of this idea to $n$-th order (central) moments? Basically I live in a world where the pain of outliers vastly exceeds the pain of ...
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1answer
154 views

How do I generate numbers according to a Robust Soliton distribution?

I'm working on project in Matlab which aim is to demonstrate how Luby Transform codes work. I need to generate generation matrix and I need to get some values from Robust Soliton Distribution, can ...
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32 views

An alternative form of $L$-estimators

$L$-estimators are based on the ordered observations $X_{(1)} \leq X_{(2)} \leq \ldots \leq X_{(n)}$ of the random sample $X_1, X_2, \ldots , X_n$. The general $L$-estimtor can be written in the form: ...
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Sandwich covariance for robust regression using M estimators for data exhibiting heteroskedasticity

Following the answer and comments on Python Statsmodels Testing Coefficients from Robust Linear Model based on M-Estimators: I'm wondering how the sandwich form of an m estimator's covariance matrix ...