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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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Can we estimate the mean of an asymmetric distribution in an unbiased and robust manner?

Suppose I have i.i.d. samples $X_1, \cdots, X_n$ from some unknown distribution $F$ and I wish to estimate the mean $\mu=\mu(F)$ of that distribution and I insist that the estimator be unbiased - i.e.,...
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What are the units of a medcouple?

Let's say I have a distribution of some weights in kg. I want to estimate the skewness of this distribution using a robust statistic, the medcouple [ G. Brys; M. Hubert; A. Struyf (2004). A robust ...
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How to report robust anovas (WRS2::t2way and t3way): no df

I have done experiments with a parasitic wasp species, comparing its life table parameters (response variables: longevity (in days), number of offspring and development time of offspring (in days)) ...
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Bayesian updating with multiple priors and multiple likelihood functions

$\Omega$ (finite) state space, $S$ (finite) signal space. Suppose we have a closed and convex set of priors $\mathcal{M}\subseteq \Delta(\Omega)$ such that each of them has full support. Let $\...
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SPSS ANCOVA with robust standard errors estimates

I am using SPSS version 25 to run an ANCOVA with heteroskedastic-consistent standard errors estimators (HC3 procedure) and I am puzzled by some of the output I get. I am fine with the robust standard ...
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165 views

Why do we use squared deviations to compute the SD, given that it amplifies the effect of outliers? [duplicate]

Suppose I have the following hypothetical data: One thousand times value 15 (i.e., 15 occurs 1000 times) and a single outlier value - 115 (i.e., 115 occurs just once - an outlier) Thus the mean is: $...
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Robust meta-analysis with robumeta package in R

I used the samples' mean ages as a moderating variable for a meta-analysis on the relationship between two variables. I used the robumeta package and I found the mean age in 20 of the 21 studies (the ...
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use and misuse of Winsorization

I am doing research on Winsorization (and trimming), which has been broadly applied in many fields, but I think many researchers didn't do it in a "rigorous" way. Or maybe even worse, they misuse it. ...
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What are some good robust loss functions for binary classification using LDA?

I am doing a project where I use LDA for binary classification. I want to know how it performs when there are outliers. What are some good robust loss functions for binary classification?
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Meaning of the low rank matrix in robust pca (rpca) particularly within a time series

I understand that RPCA tries to split a matrix into a low rank component and a sparse component. My understanding is that when we do normal PCA we reconstruct the data using fewer basis vectors than ...
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Neural Network Robust to Random Error in training set

I have read that deep learning algorithms are robust to random errors in the training set - is anyone able to explain why this is?
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Open implementation of Xu, Caramis and Mannor's outlier-robust PCA?

The answer linked below discusses an outlier-tolerant PCA method. Is there a publicly available implementation? https://stats.stackexchange.com/a/71928/86176 Here's the paper: Xu, H., Caramanis, C....
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Reference line for QQPlots: robust regression vs quartiles method

Using the car package, I drew two qqPlots of 144 p values from correlated tests on one dataset. The top plot uses a reference line drawn by "quartiles" and the bottom plot uses a line drawn by "robust"...
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What do they mean by Robust Cross-Validation?

I was reading a Kaggler Interview article and they kept specifying the importance of a stable and good cross-validation in order to win their competitions. What do they mean by that? I usually just ...
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R code for robust ridge regression

I am having trouble in searching for the MSE value in using robust ridge regression. The robust estimators that i used is LTS and MM. However, when both robust estimators were applied to ridge, the ...
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Robustness checks vs. BMA

I have a simple question. Let's say I have a model with 13 IVs and I am using a BMA for analysis. At the end, I would like to add few other variables for robustness checks. However, isn't BMA by ...
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M-estimator (S- and MM-) for regression models

Let's assume simple regression model $y_{i}=\beta_{0}+\beta_{1}x_{i}+\varepsilon_{i}$. It is obvious that the interpretation of the $\beta_{1}$ parameter is given by $\frac{\partial E(y_{i}|x_{i})}{\...
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Numerically Distinguish Between Real Correlation and Artifact

I'm looking at correlation for a large number of vectors, and many (about 3000) of these pairwise comparisons appear to have a significant correlation even after Bonferroni correction. Plotting these ...
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Discussion of Robustness

I have to include a discussion of robustness in my report. What are ways to discuss the robustness of my models? I run several logit models. But I don't know how to include something about the ...
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1answer
54 views

How to calculate the standard average of a set excluding outliers? [closed]

I have a set of numbers, and I need to calculate their average excluding outlier values (which I don't know a priori). It came to mind that many years ago I studied Standard Deviation. Could I apply ...
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1answer
72 views

Robust analogues of Mean, CV and Skewness

I need to characterize the mean, CV and skewness of my observed data (it is gamma-like distributed). This data is an artifact (outliers) enriched, so I decide to use robust statistics: median, ...
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If we change only one value of a data set, will the mean absolute deviation behave in the same way as standard deviation?

I took the new data as b and the data removed as a and calculated the new mean and used that to find the new mean and deviation in terms of the old. But it gets too complicated and there is no way to ...
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Why robust PCA results change with each run?

According to Filzmoser et al. 2009, the best way to conduct a principal component analysis for compositional data with outliers is: using a robust PCA method and using the isometric log ratio ...
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1answer
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How to model which fixed effect is most responsible for variation in the DV?

Let's say I have data on firm revenue among multinational firms. I want to test the question of what explains more variation in revenue: firm culture or country-culture. A bit confused as to the ...
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Understanding MCD

I have recently stumpled upon the robust MCD (Minimal Covariance Determinant) Estimator. If I have $n$ datapoints of dimension $p$. Let`s say we want to obtain a robust estimate for the Covariance ...
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Tradeoffs of robust mean measures (trimmed, Huber, cosh, etc)

After recently having delved into the world of robust measures (for location, mean being the classical case), I have had difficulty understanding robust measures' core dynamic. Basically, what are ...
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Robust Regression in MATLAB's robustfit: what is the optimal weight function to tackle heteroskedasticity?

I'm currently performing a linear regression analysis and encountered a fair amount of heteroskedasticity. Increases in predicted values go along with decreases in residual variance. Otherwise, the ...
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Robust distance measure for correlated data

I read a paper in which the authors want to compare the overall predictive accuracy of various predictors on a set of variables by using the Mahalanobis-Distance. However the data is not even ...
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Deconvoluting an ECDF via mixed modeling

I have data with measurement error, $W_i$, with the following structure: $$W_i = \mu + \gamma_i + U_i$$ where $U_i \sim N(0, \sigma^2_i)$, with known $\sigma^2_i$, and $U_i \; \amalg \; \gamma_i$. I ...
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1answer
286 views

Robust covariance and OGK outlier detection

I'm calculating the robust covariance of a data set in order to use mahalanobis distance for outlier detection. There are few methods to calculate the covariance in the equation. Using the Fast-MCD ...
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1answer
30 views

Multiple comparison tests after using Robust method (lmrob)

I have some violation of assumptions (normality and equality of variances) is my analysis and I decided to a use robust technique (lmrob function in R). I have a continuous response, one categorical ...
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172 views

Robust regression - differences in approach (rlm and lmrob)?

I am looking to implement robust regression in R for large data (n=~500,000). The two options that come up are lmrob and rlm. ...
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Robust regression with Sandwich estimator

I understand that rlm (robust regression) addresses issues of outliers and influential observations, but does not address heteroskedasticity. I have come to learn ...
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Point Biserial Correlation

In terms of testing the assumption of normality for a Point Biserial Correlation; I have a dichotomous variable (1 = microsleep, 0 = no microsleep) and a continuous variable (number of driving events ...
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120 views

Robust alternative to exponential smoothing?

Despite being easy to calculate and understand, exponential smoothing is excessively affected by outliers and thus performs poorly when the data has a non-Gaussian probability distribution, such as a ...
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1answer
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Interpreting the robust linear regression

Is the way that we interpret the coefficients of a robust linear regression (rlm function in R) is the same as the OLS regression? Can I interpret the coefficient of a robust regression (...
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1answer
111 views

Greater than 30% outliers in small dataset - what to do? Standard test? Test with outliers removed? Robust statistics?

I have a small-sample dataset representing observations from a longitudinal study. My principal interest is in 'change scores' across three parameters (A, B, C). This requires simple paired t-tests. ...
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($L_2$) distance for noisy data

I'm given a subspace $V$ and a set of $n$ corrupted observations $\tilde{x}_1 = x_1 +\epsilon_1,...,\tilde{x}_n = x_n + \epsilon_n \in \mathbb{R}^D$. Assume $D$ is large and that $\epsilon_i \sim N(0, ...
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Compare models with robust methds - R

This question is the first part of a larger question that is continued here. I thought that it could be easier to split it into two questions to generate better answer to both and to help further ...
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Using bootstrap for robust estimation

I am hoping to understand the process of bootstrapping outlier-contaminated data, and the effects on (simple) OLS estimators. In particular, we have a DGP, $$Y_t = \beta X_t + \epsilon_t$$ where $\...
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1answer
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Ridge Regression as Robust Optimization

We were told to assume in class that the below optimization formulations are equivalent- $$\min_w\max_{\delta:||\delta||_F\leq\epsilon}||(X+\delta)w-y||_2^2$$ $$\min_{w}||Xw-y||_2^2+\lambda||w||_2^2 ...
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Robust estimators better than the median?

I am taking samples from a large population. The samples can be of five, ten, or twenty items. I have read that Tukey's trimean is better than the median. Is that true? Are there any other ...
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Effect sizes for nonparametric 2x2 ANOVA (pre-post experimental design)

During the writing of my thesis, I stumbled upon the following problem: My data is not normally distributed (as expected) and the sample size is small (N=26, evenly spread over a control and an ...
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Hypothesis testing - OLS v M-estimation

I am trying to determine if two regression estimates are different. The first is obtained by ordinary least squares (OLS) and the second is obtained by M-estimation. As a minimum example, fits for ...
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Skewed data: Is trimming the means necessary when using bootstrapping to compare means?

I want to compare four different groups on one dependent variable. Normally I'd do a one-way independent ANOVA, except that this time the normality assumption isn't met at all (see the below ...
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Presenting extra robustness test in oral defense of econometric work [closed]

I've submitted an econometric paper for a university course, which is now followed up by a oral defense. In it, I ran a newly suggested method on a simulated data set which yielded good results, ...
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144 views

Iterative outlier diagnostic

I am working on outlier diagnostics and I have a question about the best way to conduct them. Irrespective of the way used to define an outlier (i.e., statistical indexes, threshold), some of my ...
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2answers
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Why is it easier (in a statistical sense) to estimate standard deviation than the mean?

Way back when I was still a student, I was listening to one of my stats lecturers talk about robust statistics. He showed (on the board) a series of transformations/derivations which concludes that it ...
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Applying robust regression to complex survey data

My team is conducting an analysis using a large dataset of health data from >150 demographic and health surveys with the aim of identifying optimal metrics to quantify early childhood growth at the ...
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Bootstrap for differentiable statistical functionals

I am following Parr 1985: The bootstrap: Some large sample theory and connections with robustness. The author stats that his theorem works for functional type estimators. I am trying to find a class ...