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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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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How to calculate Hodges-Lehmann estimator of slope in rank regression?

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+\...
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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 ...
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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 ...
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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 $\...
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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 ...
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PCA vs Robust PCA

Apart from that robust PCA ignores the outliers, how can you say it differs or is advantageous to standard PCA?
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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 ...
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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 ...
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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 ...
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Robust wave variograms

I am reading a research paper Eyer 1999 in which they characterize variable stars using Robust wave variograms so what is mean by Robust wave variogram and how can we analyze time series of any data (...
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What are some online algorithms for robust measures of scale?

I've found good robust measures of scale, and I've found one or two good online algorithms for robust measures of location, but I haven't been able to find an online algorithm for a robust measure of ...
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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 ...
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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, ...
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convert R2 score from sklearn (variance score) to the R squared coefficient?

I am trying to run RANSAC robust fit method on my data and predict correlation between my X and Y data. I have decided to use this method because in my small dataset I have identified one outlier. I ...
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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-...
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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 ...
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Improving robustness of XGBoost on large tabular dataset with small signal and lots of noise

I have been working with XGBoost on a large set of panel data. There are 20m+ rows with 200 features. The data includes weather related data points for 100s of cities, recorded every day, for several ...
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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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Non-adversarial robustness

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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Comparing ß-coefficients in robust linear regression between groups - different p-values between f.robftest() and lmrob() - what is the difference?

I want to evaluate if a variable predicts the change of another variable following an intervention. Therefore, I compare the linear regression lines between the intervention and control group. I tried ...
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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 latent variable models

Influence functions are a tool to study robustness. They tell us the effect of perturbing one datapoint on the trained parameters. E.g. by taking $x_i \mapsto (1+\epsilon)x_i$. How can this be used on ...
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Robustness of ELBO

The ELBO $\mathcal{L}(\phi)$ is used to quantify how good an approximate posterior $q_\phi(z|x)$ is for a dataset $x$ and an (unknown) true posterior $p_\theta(z|x)$. However this is all under the ...
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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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282 views

Is there an R function for a robust three-way mixed ANOVA?

I'm a PhD student in the social sciences and I have run into some issues analyzing my dissertation data - namely, non-normality, and to a lesser degree, heterogeneity of variance. Specifically, I am ...
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Which assumptions and constraints are relevant in a mixture model to use either a Gaussian, Weibull, Gumbel or other distribution?

For a dataset that I'm analyzing, I can obtain a series of distributions on a given feature space, and I can assume that they take the form of collections of uni-modal clusters (think of something ...
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Sampling distribution of loss function

So I believe the sampling distribution of the likelihood function is a basic idea in frequentist statistics. For example, the Fisher information $\text{Var}_x(\nabla_\theta \log P(x|\theta))$ which ...
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Are there formal measures for classifier or regression robustness?

Are there performance measures that produce a numerical value of the robustness of a classifier or regression. By robustness I mean graceful degradation in performance to unexpected input (similar to ...
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Robust regression for heavy-tailed random design

As far as I know, there are robust regression methods for outliers in response $Y$ and heavy-tailed error $\epsilon$. The settings for the design matrix (predictor) $X$ is either fixed design or sub-...
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Winsorized mean - trimming furthest points instead of both endpoints

I'm wondering if the Winsorized mean can be improved by trimming the 5% farthest points from the mean instead of trimming 5% on each endpoint. Concretely: Consider the Winsorized mean, where we ...
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Challenging robustness to violations of multivariate normality

I am generating multivariate normal (MVN) data and evaluating power of MANOVA in R. For instance, I simulate a factor A with two levels, and obtain $\boldsymbol{y}_{A_1} \sim MVN(\boldsymbol{\mu_1}, \...
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Jackknifing for assessing the "robustness" of test results

In a presentation I saw recently, a two-sided t-test was repeated with jackknifed subsets of the original data in order to assess the result's "robustness". In detail, they took a random ...
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Optimization function of the Hodges-Lehmann location estimator

The median minimizes the sum of absolute differences while the mean minimizes the sum of square distances. What is the function which is minimized by the Hodges-Lehmann location estimator?
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Is traditional negative binomial regression robust to model misspecification or not?

By "traditional" NBR I mean NB2, i.e. the one modeling variance as a quadratic function of the mean, with the formula: $Var(Y)=E[Y]*(1+\alpha*E[Y])$. I have found contrasting statements in ...
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Trimmed, weighted mean

The trimmed mean (or truncated mean) is a robust version of the mean, designed to be robust to outliers. I am wondering what is the right trimmed version of a weighted average. If I have a sample ...
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How to robustly present a min and a max value?

I have a set of measurements from an air polution sensor. I want to determine the min and the max value in a period of time (let's say in a day). The min and the max don't have to be the true ...
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Instrumental Variable - clustering and standard errors, in both stages?

I was wondering whether in an instrumental variable procedure, you do the clustering and standard errors in both stages or just the final stage. Wooldridge (fifth edition, section 15.6) in the first ...
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Is there a measure of the robustness of a statistic?

I got a question today when talking about mean and median, IQR and variance. Is there a numerical measure of the robustness of a statistic? I must confess that I had never thought about that before, ...
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When to use robust one-way repeated measure design ANOVA?

I have a set of 9 different factor levels from my independent variable to be compared against each other. Here are the results of the different assumption tests in R. I'm just going through my ...
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Interpretation Robustness Check table

we conducted our robustness check for our negative binomial regression using "checkrob" command in Stata (Barslund, Rand, Tarp; 2007). As a result we got the following table. How can I tell ...
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How to clean up outliers in regression which cannot be visualized?

Recently I meet a problem in an interview. Given a dataset $\{(X_i, y_i) \}$ for regression problem, how to detect and clean up outliers before starting using any regression algorithm. The following ...
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92 views

Post hoc test for robust mixed design ANOVA using R

I have calculated a robust mixed ANOVA because I have no homogeneity of the error variances nor of the covariances (with a 2 level between-subject and a 2 level within-subject variable). Can I ...
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63 views

In general, how to determine the weight function of Robust regression

I think the question is clear from the title. How the weight function for example in Huber is calculated? Is it by differentiating the objective function?
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51 views

Weibull with known shape parameter

I am new to Bayesian robustness. If I have Weibull likelihood $X$~ Weibull($\lambda$, $\beta$)$= \lambda \beta x^{-\beta} \exp(-\lambda x^\beta)$ with $\lambda$ unknown and $\beta$ known. we know that ...
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NA values when converting into wide format for Wilcox's robust ANOVA

I have a dataset of more than 10.000 values, with 12 different factor levels that are NOT evenly distributed. For my dataset, Levene's test is very significant which means that the assumption of ...
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Can we ALWAYS assume normal distribution if n >30?

I'm in a debate with a coworker and I'm starting to wonder if I'm wrong but the internet is confusing me more. We have continuous data [0,infinity) that is retrospectively selected on individuals. The ...

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