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

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When do improper linear models get robustly beautiful?

Improper linear models are described from time to time in the literature. In general, such models can be described as $$ y = a + b \sum_i w_i x_i + \varepsilon $$ what makes them different from ...
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Need help understanding this algorithm for a robust estimator for Geom. dist

I am trying to figure out a way to estimate the parameter for a Geometric distribution, using a random sample that is influenced by outliers. Searching through previous questions/answers, I saw this: ...
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Post hoc test for robust 3 way ANOVA

I am doing a 3x2x2 between subject study. To make thing simple, I name my variables as A, B and C here. Using the WRS 2 package in R, I have gotten results for the ...
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Robust Estimators - Winsorized Variance degree of freedom (df)

this is my first question on this site. So, I'm currently working on my final year thesis, and it was on Robust statistics. In my work, I will use Trimmed Mean, Winsorized Mean and Winsorized ...
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25 views

3way between subjects Anova with Unbalanced samples

I would like to perform robust 3-way ANOVA using the WRS package in R. The very first requirement is to cast the data into wide format. Hence, I have wide format data frame with unbalanced rows in ...
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Calculating and plotting confidence interval for Theil-Sen estimator

I'm using Wilcox's R functions (specifically, regplot) to plot a Theil-Sen estimator with a single predictor. However, regplot ...
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93 views

How to select the 'best' trim value for the mean function?

I'm experimenting with the trim parameter to the mean function, E.g. ...
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11 views

Experimental Design Optimal allocation to treatment

I have trying to design an pre-post study on the effectiveness of a particular media platform in inducing behavior change. The 700 households are distributed in 6 geographical clusters. They have ...
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53 views

Text mining: Robust correlation or similarity measures

I'm currently using word_cor function (qdap package). I observed that the function is not robust as it implements Pearson, Spearman and Kendall measures only: non-occurrence of both words (in the ...
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1answer
43 views

Changes in F-value of instrument

I am using 2SLS to estimate the effect of education on the probability that one works. In the first stage I regress education on my instrument and the other exogenous control variables. The same ...
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110 views

Looking for a robust, distribution-free/nonparametric distance between multivariate samples

There are many distance functions for distributions out there, but I'm having a hard time wading through them all to find one that is "distribution-free", or "nonparametric", by which I mean only ...
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2answers
55 views

How to downweigh outlier in a sum?

I have a simple problem. Assume following dataset: resids <- c(,9,8,7,12,14,8,9,15,4,9,10,200) n <- length(resids) p <- 2 Using this dataset I want to ...
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18 views

Comparing fixed effects regression and robust regression

I have panel data on countries' renewable energy net generation (and installed capacity) over time. I am regressing these dependent variables on various socioeconomic variables, as well as binary ...
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30 views

Testing robustness of a model glmmadmb

I would like to test the robustness of a model I made, as the summary does not feel understandable enough to me. Let me explain: I have a large dataset of conflicts with bears in Slovenia, and I ...
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how to write these two inequality? (Asymptotic properties of m estimator)

$T_n^*:=sup\{t|\sum ψ(x_i;t)\gt 0\}$ $T_n^{**}:=inf\{t|\sum ψ(x_i;t)\lt 0\}$ As it's seen in the above figure, $-\infty \lt T_n^{*} \le T_n^{**} \lt +\infty$ Then, how to show that the followings ...
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zelig package in R gives the same standard error with robust=TRUE

Any idea why robust option is not working in Zelig package? ...
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24 views

explain the interpretation of the following proposition and how to prove it?

Please explain the interpretation of the following proposition and how to prove it? Proposition: Assume that $\exists t_0 $ s.t. $\lambda(t)\gt 0 $ for $t \lt t_0$ and s.t. $\lambda(t)\lt 0 $ ...
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34 views

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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32 views

Recommend monograph on statistical model misspecification

Is there a good book on statistical model misspecification in general? It should cover, for example, the behavior of estimators (e.g., maximum likelihood) when the specified parametric family does not ...
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24 views

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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1answer
215 views

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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211 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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37 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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10 views

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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2answers
65 views

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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101 views

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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26 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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21 views

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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47 views

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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50 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
76 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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51 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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61 views

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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99 views

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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1answer
28 views

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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25 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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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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182 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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247 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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66 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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246 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 ...