# 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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### Bootstrap-based robustness of a test checking. Is resampling from sample distribution a good procedure?

I aim to check the robustness of 2 groups t-test when samples come from lightly skewed distributions. To approach the problem I though about performing a Montecarlo based robustness analysis using ...
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### The variance of the weighted median and optimal weights

The median $\tilde{\mu}$ of a sample in many ways is analogous to the sample mean $\mu$. Both are an estimate for the population median or mean respectively, and both approach a Gaussian distribution ...
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### Infinitesimal Robustness, influence function of $T$ at $F$

This text is taken from Introduction to robust estimation and hypothesis testing. Wilcox R. First I will write down the description that leads to definition of relative influence on $T(F)$ and then I ...
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### Robust distance weighted mean

Given a data sample $\{x_i\}_1^n$, instead of hard omitting outliers by e.g. trimming, one can form a weighted average where we soft penalize observations out in the tails. \begin{align} \mu = \frac{...
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### What is the difference between robustlmm and clubsandwich in R?

Excuse my ignorance, I am trying to get around a problem with my statistics that involves severe outliers issues, with heteroskeskedacity. My model using linear mixed models, in R, with repeated ...
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### Robustness checks for DiD

I am currently looking at a DiD model to evaluate the impact of a policy on ethnic and non ethnic people in the EU. I have done the regression and got the results. I have only two time periods but 10 ...
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### Robust LMM or Random Forest?

I have non-normally distributed, heteroscedacic and autocorrelated data. To overcome these issues I would like to use robust linear mixed models with the robustlmm package in R or random forest ...
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### AIC for robust generalized linear models (glm)

How can I calculate Akaike's 'An Information Criterion' with small sample size correction (AICc) for glmrob from robustbase in R?...
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### Will models selected as a linear mixed model be the best model for robust modeling?

My question is mostly theoretical but all of my analysis is in R and my models are structured to fit the lme4 package and the ...
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### Multiple Sclerosis: study design to beta test a software

I am a beta-tester of a software that is intended to help the radiologist to interpret MRI reading of Multiple Sclerosis (MS). MS is a disease that, over time, could lead to new lesions, expanding ...
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### Significant interaction in robust ANOVA but no significance in traditional ANOVA

In a 2x2 mixed design (2 groups measured at 2 times, n1 = 10, n2 = 12), a subsample violated the assumption of normality (Shapiro Wilk test). Thus, I used robust ANOVA (R-package ...
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### MinCovDet confusion

Consider the following experiment: look at Bitcoin prices for the last several years, then try to estimate the volatility, in the following two ways. Empirical trailing variance (of log returns) over ...
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### minimum determinant covariance matrix and covariance

I am trying to understand minimum determinant covariance. I gather from this stack exchange post that it tries to select a subset of data that is tightly distributed to exclude anomalies, and it does ...
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### Reporting robust means and SD to make more comparable to robustbase::glmrob results

I need to report the mean, and SD of two groups for a specific variable, as well as the odds ratio of the two groups using robust logistic regression. The variable does have outliers. I instead want ...
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### Why is 50% the best breakdown point for an estimator?

As stated in Wikipedia: Intuitively, we can understand that a breakdown point cannot exceed 50% because if more than half of the observations are contaminated, it is not possible to distinguish ...
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### Why is the Median Less Sensitive to Extreme Values Compared to the Mean?

I am sure we have all heard the following argument stated in some way or the other: For a given set of measurements (e.g. heights of students), the mean of these measurements is more "prone"...
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### Why do I get a lower R-squared value when I add more variables to my multiple linear regression?

I'm using the Regression Learner tool in MATLAB to do robust linear regression on a set of variables. However, with only one variable I get a higher R-squared value than when I'm adding one or two ...
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### Can we report an F statistic on a Robust Linear Model with only Fixed Effects?

I'm estimating a fixed effects model using Linear Regression with the Huber weighting function. I included a boxplot of the data. How do we report an F-value and significance for the entire model like ...
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### better to use robust mixed model or mixed model with multiple imputation?

I've tried to run a robust mixed model using multiple imputation, but I can't pool the estimates, as I posted here. If there isn't a way to use rlmer together with <...
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### What does it mean for a statistical test to be "robust"?

Is there an intuitive way of understanding what these two sentences mean and why they're true?: "ANOVA is 'robust' to deviations from normality with large samples", and... "ANOVA is '...
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### Confidence interval crosses 0 but statistical significance at p < 0.05 using robust post hoc tests, any explanation?

I have 12 groups so 66 contrasts, though I'm only interested in 6 of them, I'm using the mcppb20() function from Rand Wilcox's WRS package in R. I'm using 5000 bootstrap samples as suggested and 0.2 ...
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### Why should we use 16-50-84 percentile instead of $\mu$ and $\sigma$ to characterize sampling results such as MCMC

Can someone explain why we should use the 16-50-84 percentile rather than mean and standard deviation to characterize the average and uncertainties of the sampling results, such as MCMC (the Markov ...
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### Question about Huber loss when k=0 in Casella and Berger

In Casella and Berger (page484), the following Huber loss is defined. Then on the next page, Table 10.2.1 shows the Huber estimator for different $k$: In particular, $k=0$ gives the median, which ...
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### Covariance from time series with asynchronously observed components

Let $(X_t) = (X^1_t, \cdots, X^d_t)$ be a time series in $\mathbb{R}^d$ with covariance matrix $C_t := \big(\mathrm{Cov}[X^i_t, X^j_t]\big)_{i,j}$. Suppose that $X\equiv(X_t)$ satisfies some ...
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### Does blind source separation (ICA) work if channels of mixture are observed asynchronously?

Does Independent Component Analysis (ICA - fastICA, SOBI, etc.) work reliably when applied to a multidimensional mixture (observation) $X = (X^1, \cdots, X^d)$ if the different channels $X^i$ of the ...
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### Reporting robust regressions

I'm running robust regressions in R (rlm from the MASS package) for 3 different models of regressions that are all related: DV ~ IV1 + error DV ~ IV1 + IV2 + error DV ~ IV2 + error I was wondering ...
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### Why is maximum likelihood estimator suspectible to outliers?

I'm new to statistics and currently learning abot MLE. Some of the papers I read: Robust Graph Embedding with Noisy Link Weights mentioned MLEs are suspectible to contamination in data, but didn't ...
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### Robust Regression Effect Sizes

What are some ways to calculate effect size statistics from a Robust Linear Regression (Specifically one using Bisquare weighting and MM estimates)? I'm trying to find the closest equivalent of a ...
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### Robust statistics to determine the linear relation of a random varialbe to a group of other random variables

https://solvemprobler.com/blog/2015/12/19/calculating-stocks-beta-using-r/ Beta for a security is defined above. Where it is basically the slope of the linear regression of the daily return of the ...
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### Choice of constants in a robust z score

I'm trying to calculate a robust z score, and I'd like to understand the constants I'm using, and their impact on my statistic. One corner case I've noticed is when my sample happens to be all the ...
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### how to test variance of sample mean for very skewed distribution?

The underlying distribution is not known explicitly but rather inferred from a sample of around 10 million cases. It represents the cost of something and after normalizing the mean to 1 it has the ...
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Suppose we have $n$ paired observations $(x_1,y_1),(x_2,y_2),\ldots,(x_n,y_n)$, where $y$ is the response variable and $x$ is the covariate. Consider a simple linear regression model $$y_i=\alpha+\... • 9,120 2 votes 1 answer 50 views ### Robust linear regression for complex valued data in R Are there any existing R packages capable of performing a robust linear regression on complex valued data? I have a set Y of complex valued (a + b i) data, that are linearly dependent on another ... 2 votes 0 answers 41 views ### Which modern robust methods should be used (under what circumstances/as a standard)? [closed] I started reading about modern robust methods as an alternative to classic parametric techniques because I keep encountering issues with normality and, at times, violations of other classic parametric ... • 625 1 vote 1 answer 134 views ### What is the medoid function and its relation to the median? The medoid function is defined in this graph neural network paper as:$$ t := \arg\min_{y\in \mathcal{X}}\sum_{j=1}^N||x_j-y||$$which is a "multivariate generalization of the Median" and \... • 31 1 vote 0 answers 23 views ### Suitable definition of breakdown point for estimators of bounded statistics (i.e constrained estimation) Let \Theta be a nonempty compact subset of \mathbb R^d. For example, the reader may think of the closed unit-ball \Theta := \{\theta \in \mathbb R^d \mid \|\theta\|_2 \le 1\}. Consider an ... • 468 1 vote 0 answers 43 views ### PCA vs Robust PCA Apart from that robust PCA ignores the outliers, how can you say it differs or is advantageous to standard PCA? • 379 2 votes 2 answers 67 views ### Interpreting mixed effects model results. Why are my coefficients for mixed effects model are so large? I am an economics grad student and I am in the process of writing a paper disproving using the Gini coefficient as a solitary measure of income inequality in migration determinants analysis. I have ... • 21 0 votes 0 answers 40 views ### I have a question regarding the robustness of the T test for two for independent samples I have a large sample, 200 participants in each group, and normality is violated (the shapiro-wilk test showed that all data were non- normally distributed p<0.05) but i assume that can still ... 0 votes 0 answers 24 views ### Statistical Method for Large Data Sets: Obtain Means via Clustering I seek a sanity check on a technique I developed to characterize reasonably large data sets with a single statistic each. The data are pause duration measurements taken during 20-minute open field ... 0 votes 1 answer 167 views ### Robustness check for cross-sectional data by merging data sets and creating year dummy variable I am currently working on the effects of maternal education on child mortality with cross-sectional data. I got data sets for 2008, 2010 and 2014. I am thinking of doing a robustness checks and I ... 0 votes 1 answer 43 views ### Convex set of huber's contamination model In the celebrated Huber's robust estimation paper, he considered the following model x_i \sim (1-\epsilon) P_\theta + \epsilon G where P_\theta is assume to be standard normal. Under this model, ... • 55 1 vote 0 answers 19 views ### Robustness of the Brown–Forsythe test against a change of skewness or other moments Consider the case of two random variables obeying log-normal distributions. Suppose that the \mu parameters are equal but the \sigma parameters aren't. This would imply that not only the variances-... • 11 1 vote 1 answer 54 views ### Which Robust fit method to apply to exclude single outliers? I got some data samples (a,b) and I am trying to calculate correlation between a and b. As I am new in this type of analysis, I have calculated Rsquared with linear regression method and got 0.5 as ... • 25 8 votes 1 answer 530 views ### Are Bayesian methods robust to violations of normality? Consider the simple case$$x|\sigma^2 \sim N(0,\sigma^2)\sigma^2\sim IG(\alpha,\beta) Then, marginally, $f(x) \propto (\beta + x^2/2)^{-\alpha}$, is a t-distribution. Does this mean that the ...
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One measure of an estimator's robustness is the breakdown point, which tells us how many adversarial observations are necessary to make the estimator useless. However, is there a notion of non-...
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### Estimators of location and scale versus mean and variance

This question is rather semantic than statistical. In Robust Statistics, estimators of mean and variance of a distribution are often called respectively "estimators of location" and "...
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### Are robustness and generalizability the same thing?

An optimal parameter $\theta^*$ is robust if it does not change much when calculated for different samples of data from a population. $\theta^*$ has good generalizability if its predictive power ...
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### Robustness of MAP estimate

In Bayesian inference, we have a dataset $x$ and assumed to come from a known parameterized distribution with unknown parameters $\theta$. We then seek to maximize the posterior $P(\theta|x)$ in order ...
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