# Questions tagged [robust]

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

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### Which reference could I cite for using confidence intervals instead of P-values when using robust linear mixed models (R package: robustlmm)?

I am using the R package robustlmm for some analysis due to its characteristics. I have read in posts like this one that with this type of models is better to use confidence intervals than $p$-values, ...
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### If we are taught to not remove outliers without investigation, how do robust methods (median, trimmed mean) can be even suggested?

I just saw an article, which taught to nor remove outliers without investigation, because it may be a unusual but valid observation or naturally skewed data, for example in chemistry or medicine. Only ...
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### Simple GLMMs with imperfect fit---are they robust?

I'm wondering if there is a good and accessible discussion of how robust GLMMs of imperfect fit (e.g. some patterns in residuals) are in simple models, for instance those where repeated measures ANOVA ...
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### Robust regression coefficients replication

I am trying to perform a robust regression using the LMS (least median of squares) method. For some reason, I just can't seem to replicate the results the book is showing. The data set the book is ...
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### why linear regression gives high mean squared error with robust scaler?

I've been trying to use a pipeline that consists of robust scaler and one of the algorithms like xgboost, ridge, lasso, and linear regression, and they all give better results except for linear ...
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### Two-group “ANCOVA” with Theil-Sen?

("ANCOVA" might typically refer to using at least three groups. In what I do, I am always comparing two groups, and that is what I mean throughout this question.) I know how to do ANCOVA via OLS ...
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### Measure “concentratedness” of 1D data

I have $N$ datapoint dataset $\{x_i, y_i\}$, where $x_i$ are equally spaced over the interval $[0, 1]$, and $y_i$ are non-negative. It is known that $y_i$ is a sum of a signal and gaussian noise. The ...
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### Discrepancies in robust ancova calculated in R with the WRS2 package vs by hand

I've conducted a study where participants in 2 groups (Control and Experimental) completed three scales (NJ, A, and D) at two time points (T1 and T2). I'm running ANCOVAs with the T2 responses as my ...
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### In regression modeling, are there any caveats to always using robust standard errors?

Aside from efficiency issues, is there anything else to this?
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### Does the sigma-clipped variance/standard-deviation count as a robust estimator of scale?

Robust estimators of scale, such as the median absolute deviation (MAD) and so on, are less affected by outliers than something like the basic standard deviation/variance. Firstly, is there a specific ...
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### CV score for robust estimators

I am working with Theil-Sen Regression, which is a robust estimator of parameters in linear regression. For the implementation, see, for example, https://scikit-learn.org/stable/auto_examples/...
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### What is a more robust estimator than Least Squares and Least Absolute Deviation?

I am trying to fit a model using rather limited data with non-linear least squares and least absolute deviation approach. My problem is that both estimators are not very robust, and so bootstrap and ...
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### Theil–Sen estimator

I am working with Theil–Sen estimator for robust estimation of a slope of univariate linear regression. The size of dataset is about 150. I use Python to fit it sklearn.linear_model.TheilSenRegressor ...
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### Robust Bootstrapped tests (ANOVA, T test)

I am reading into robust tests and one of the questions that I have revolve around the bootstrapped version of robust tests. For instance, in addition to the Yuen t test based on trimmed means, there ...
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### Fast robust location and scale estimate in python

I am looking for a python package performing robust estimate of location (and possibly also of scale), using M-estimator with Huber or Tukey weights. Background I have implemented both estimators in ...
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### Calculate standardized regression coefficients and R^2 with robust standard errors

for a project I am calculating multiple regressions. In all models I had problems with heteroscedasticity. Since my sample size is large I calculated robust standard errors to deal with this problem. ...
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### Model Comparison Tests with Bootstrapped Models

I've found myself in a catch-22 of wanting to conduct model comparison tests (like the Likelihood Ratio Test) but having to accommodate non-normal data. I know the LR test is invalid with Robust ...
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### My simple regression is homoscedastic - should I use robust standard errors or both?

I've been asked to estimate the following simple regression with the 'appropriate' standard errors at 5% sig level and report the results in a table: ...
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### Estimating mean: Median vs. Huber

Is it a good idea to use Huber, Tukey or similar weighting function for estimating robust mean? What are the advantages/disadvantages of using such an estimate vs. using median (I am particularly ...
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### Breakdown of the median

I am looking for an accessible review of the breakdown properties of the median (estimator of location) and possible practical solutions for dealing with it. (By accessible I mean short and readable ...
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### Robust regression vs bootstrapping of confidence intervals

In multiple regression, when the independent variable is not normally distributed and the dependent variable is not normally distributed, is bootstrapping of the confidence intervals or robust ...
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### How to interpret the output from the robust regression in terms of the expected value?

Regression is a way to model the relationship between the conditional expected value and the predictors. But in the robust regression we don't have the expected value (say, arithmetic mean for ...
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### Address unequal variance between groups before applying contrasts for a linear model? (r)

My Goal: I have an ordinal factor variable (5 levels) to which I would like to apply contrasts to test for a linear trend. However, the factor groups have heterogeneity of variance. What I've done: ...
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### More robust measure than Mean

I am currently dealing with data with many outliers and I shall not to eliminate them from the data for analytical purposes. What measure shall I use to describe central tendency of the data yet with ...
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### How robust is coxph when the proportional hazards assumption is violated?

How robust is the coxph when I don’t have proportional hazards? How common is non prop hazards and how do I fix it? Does transforming variables help? Does non parametric survival analysis handle non ...
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### Identifying an algorithm described as 'Tukey approach' for ignoring outliers?

MVTec's machine vision library Halcon has an operator fit_line_contour_xld for robustly fitting lines to 2D points. Here's the documentation entry for that operator:...
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### How do I estimate the robust standard errors by hand with coefficients as factors?

I am trying to manually calculate the standard errors for two coefficients. My original regression is something like: regress meaneducstate (a factor) meaneducpum (a factor) and education level on ...
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### Who first invented/proposed/formulated the IQM (Interquartile Mean) and the Truncated/Trimmed Mean?

I've looked this up on google for quite some time but couldn't find the answer! Does any of you know who or how can I find who first proposed these statistics? How can access their respective ...
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### Why do robust linear models give smaller standard errors?

I've always read and been told that for heteroskedastic errors a normal OLS fit will generate standard errors that are too small, leading to a false degree of confidence in coefficient estimates. ...
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### Calculating orthogonal distance and score distance from robust PCA in python

Having found the following python implementation of the robust PCA algorithm link I am keen to use this to recover the orthogonal distance (OD) and score distance (SD) for my samples as per this ...
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### Distinguishing Bad Leverage Points from Vertical Outliers

Going through Regression class notes (written mostly following Kutner`s book, I believe), there was a brief display of how, in some cases, robust residual plots (such as standardized LTS residuals), ...
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### Addtional parameter of Huber regression

In Huber regression, there is a delta parameter in it's mathematical formula. Now, performing this regression in R can be done through the function rlm and with <...
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### Robust Statistics for Finance with focus on Outliers

There's Robust Statistics with things like using median instead of mean to ignore outliers (usually considered as errors that should be ingored). ... Robust statistics are statistics with good ...
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### What are some of the robustness checks for the likelihood ratio test?

In the application of statistical methods in social science, one usually does a lot of robustness checks. If I got some publishable findings using LRT test by discrimination two theoretical models, ...
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### Pairwise Comparisons for Rank Based rfit Models in emmeans

I recently found this package: https://journal.r-project.org/archive/2012-2/RJournal_2012-2_Kloke+McKean.pdf. I am utilizing this package for Robust Regression without having to resort to M or MM-...
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### Asymmetric robust regression

What are the methods for robust regression with asymmetric distribution of outliers? I am specifically interested in equivalents of Huber and Tukey M-estimators. However, asymmetric heavy-tailed ...
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### Outlier detection with EM

I am interested in using expectation maximization for outlier detection. In the literature this is usually done assuming that the data of interest are normally distributed while the outliers are ...
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### Using expectation maximization for robust regression

What are the advantages/disadvantages of using EM for robust estimation vs. the robust estimation with Huber or Tukey loss functions?
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### When to use RANSAC?

Does it make sense to use RANSAC-type algorithms (RANSAC, MSAC, MLESAC, etc.) for small data sets (20-30 points)? On the one hand, all the points need to be accounted for and this can be done with ...
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### Use both historical prices and fundamentals data for predicting portfolio profit?

Get highly accurate probability distribution for the future price of portfolio using all the data available. Each stock has two historical data - daily prices (scalar time series updated daily) and ...
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### Robust sum of non-independent random variables

What approach could be used to sum non-independent variables? I have probability distributions of stock prices and want to calculate the probability distribution of the portfolio price (sum of some ...
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### HAC Confidence Interval in Interrupted Time Series

I have a dataset about quarterly deaths over the last 18 years (Q1 2000-Q4 2018). In Q3 2004 there was a policy change which might had lead to an increase in the number of deaths. I fitted an ...
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### Robust regression with M-estimators

I have a couple of question regarding robust regression with M-estimators, such as Huber estimator or Tukey biweight estimator: Is it possible/common to combine these with regularization terms, such ...
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### Generation of simulated data [closed]

I want to generate some data . For example I would generate three variables.2 Independent,1 dependent.
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### How can robust regression be used with penalty functions for sparse solutions?

I don't seem to see robust regression used with penalty functions for variable selection, either L1 or Huber can't use mathematica's Fit at the same time
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### Robust common mean inference

In an ANOVA-like setting I have several groups of variables that I expect to have the same mean, $\mu$. Quite often some of the groups would have shifted means, $\mu + \Delta$, due to effects beyond ...
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### Breaking point of a measurement system

I am trying to calculate the following measurement system breaking point: we have a summary of some kind of experiment X of size n. Now we are trying to find the number of changes in the summary it ...
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### Relationship between expected absolute deviation and standard deviation

The standard deviation of a random variable $X$, $$\sigma = \sqrt{Var[{X}]} = \sqrt{E[X^2 - E[X]^2]}$$ is a very commonly used measure of "normal" distance from the mean of $X$. A much less frequently ...