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

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Book suggestions - robust regression

I'm start to study M estimator - Robust Statistics. Can you suggest sound books for this topic? Note that I have Huber's books. Thank you.
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Why does a robust linear model fitting give a residual standard error?

The way I understood when to use a a robust linear fitting is for example when your variance is not constant (e.g. when you have heteroscedasticity as shown with a Breusch-Pagan test for example) or ...
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P values of coefficients in rlm robust regression

I am using rlm robust linear regression of MASS package on modified iris data set as follows: ...
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184 views

Why not robust regression everytime?

Examples of this page show that simple regression is markedly affected by outliers and this can be overcome by techniques of robust regression: ...
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28 views

Non parametric test for ANOVA and coefficient of variation

Which is equivalent non parametric test for one way ANOVA ? Is quartile coefficient of dispersion for non parametric test equivalent to coefficient of variation (COV)? Among them which measures are ...
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Influence function for inequality index using ordinal data

I wonder whether it is possible to derive influence function (explained for example here: Influence functions and OLS) for an inequality index designed for ordinal (non-continuous) data in this ...
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Specific robust measure of scale

Do you know of any outlier resistant measure of scale $R(Y_1, \dots, Y_n)$ with the following property related to the sample standard deviation $S$? Magic property: If $S(Y_1, \dots, Y_n) > 0, ...
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Geometry of robust linear model

$L_2$ minimisation has a very nice geometric explanation as projection onto a subspace of the appropriate size. Is there a similar "real explanation" for any of the approaches to robust regression? ...
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16 views

Can you exclude one country as robustness check in multilevel cross-country model?

I am conducting a multilevel study in which individuals are nested in countries. As a common robustness check in normal linear regressions, we can exclude one or a few countries with special ...
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How to account for correlation among all observations in my sample?

To illustrate, consider a group of students who take a math exam, but who also cheat during the exam. I wanted to run a regression of whether the students passed the exam (dichotomous dependent ...
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Adjusting for outlier in Fractional logit in R when dv is very small proportion

I used the code from this site: http://stackoverflow.com/questions/19893133/fractional-logit-model-r to estimate a fractional logit model. There are 90 observations in my dataMy dependent variable is ...
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GARCH estimation, reduce outlier effect with t distribution

I am trying to estimate GARCH(1, 1) using MLE. As my data contains a lot of outliers, I think using t distribution to represent errors makes a lot of sense. But I am completely lost at how to ...
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Huber's M estimator for contaminated Gaussian noise

Huber discussed in this seminal paper "Robust Estimation of a Location Parameter" link that if we have some observations $x_i$ as follows: $$y_i = \theta + \nu_i, ~~i=1,\cdots,N, \tag{1}$$ where ...
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Prediction Intervals for Robust Regression: Formulation and are they larger than for OLS?

I have created regression models using robust regression - in particular, LTS and MM-estimators (using the R package robustbase). I am now looking to creation prediction intervals. The standard ...
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33 views

Robust Measures for Forecast Accuracy

I am doing a forecast using robust exponential smoothing methods and to determine / measure the forecast accuracy I want to use robust measurements as well. As I am not really familiar with robust ...
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1answer
60 views

Non-robustness of parametric statistics

Why is parametric test considered to be non-robust ? Or, why is parametric test not considered to be robust?
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39 views

How to correct heteroskedasticity in linear model of probability?

If we fit linear regression model to data, where dependent variable is binary response, then heteroskedasticity occours, how to correct for this issue ? Is it different then correcting for ...
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Does MCD estimator suffers from swamping effect?

If there are multiple outliers in the data set, the Mahalanobis distance suffers from masking and swamping effects. In order to rectify this problem, robust estimation of location and scale, such as ...
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M-estimators: textbook examples

I would like to practice with solving M-estimators problems, but I cannot find where they are easily explained. Could you please recommend me something? Thank you very much for any help!
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Handling outliers in Bayesian linear regression

I am reading this post which talks about Robust Linear regression in a Bayesian setting. The particular blog post can be found here: http://twiecki.github.io/blog/2013/08/27/bayesian-glms-2/ There ...
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Solution to exercice 2.2a.16 of “Robust Statistics: The Approach Based on Influence Functions”

On page 180 of Robust Statistics: The Approach Based on Influence Functions one finds the following question: 16: Show that for location-invariant estimators always ...
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heteroskedasticity in logit/cox

I am using a logit and a cox proportional hazard model for my analysis, and the newest version of Stata. I have found that there are no tests to check for heteroskedasticity for logit/probit models, ...
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Why do we care so much about normally distributed error terms (and homoskedasticity) in linear regression when we don't have to?

I suppose I get frustrated every time I hear someone say that non-normality of residuals and /or heteroskedasticity violates OLS assumptions. To estimate parameters in an OLS model neither of these ...
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Confidence Intervals for a relative risk where i lack the underlying data

I have two estimated rates and their 95% confidence intervals but not the underlying data. I take the ratio of the two to get a relative risk, but how do I determine the 95% confidence intervals for ...
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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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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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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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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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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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190 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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61 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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152 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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64 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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122 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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129 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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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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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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255 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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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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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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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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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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122 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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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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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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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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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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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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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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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: ...