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

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Robust variance estimators

Given $N$ data points in $\mathbb{R}^p$ - some of which are outliers (drawn from a different distribution from the inliers) - what sorts of algorithms have been designed to estimate the robust ...
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1answer
13 views

F-test formula under robust standard error

I am attempting to write a program that will (among other things) use the F-test in multivariate regression under standard robust errors. I am having trouble finding a specific formula for the ...
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12 views

How should I choose WLS weights with categorical IVs?

I have a 2X2 design (2 categorical independent variables (IVs) with 2 levels each), and a single dependent variable (DV). I have 91 samples in total with these cell counts: 30, 19. 20, 22. My data for ...
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40 views

Robust regression goodness of fit

I'm using R to compute robust multiple linear regression. I use the command rlm from the package MASS. As psi function I use ...
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1answer
131 views

What is the minimum viable cell size for 2x2 ANOVA?

I have a 2x2, between-subjects experimental design (2 independent variables (IVs) with 2 levels each) and one dependent variable (DV). My data are unbalanced and an interaction between the IVs seems ...
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35 views

Differences between robustness checks and sensitivity analysis

This is a bit of a terminology question, but what is the difference between a robustness check and a sensitivity analysis? For example, if performing analysis to see how sensitive (or robust) a ...
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17 views

Is there a generalization of trimean to $n$-th order (central) moments?

I think trimean is the cat's meow. Is there a generalization of this idea to $n$-th order (central) moments? Basically I live in a world where the pain of outliers vastly exceeds the pain of ...
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30 views

How do I generate numbers according to a Robust Soliton distribution?

I'm working on project in Matlab which aim is to demonstrate how Luby Transform codes work. I need to generate generation matrix and I need to get some values from Robust Soliton Distribution, can ...
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26 views

An alternative form of $L$-estimators

$L$-estimators are based on the ordered observations $X_{(1)} \leq X_{(2)} \leq \ldots \leq X_{(n)}$ of the random sample $X_1, X_2, \ldots , X_n$. The general $L$-estimtor can be written in the form: ...
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2answers
49 views

Advice for interpolating a model

I'm new in Stack Exchange, so I hope no to be off topic. I'm also new in bioinformatics and I was asked to perform an analysis. Briefly, I have a dataset of 29 cell lines and the IC50 values of a test ...
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37 views

Sandwich covariance for robust regression using M estimators for data exhibiting heteroskedasticity

Following the answer and comments on Python Statsmodels Testing Coefficients from Robust Linear Model based on M-Estimators: I'm wondering how the sandwich form of an m estimator's covariance matrix ...
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1answer
89 views

The Effect of Outliers

The following question comes up in robust statistics. There are two formula indicated below that I do NOT know how to derive. However, in order to make the context clear, let's start with the easiest ...
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1answer
94 views

Is a weighted $R^2$ in robust linear model meaningful for goodness of fit analysis?

I estimated a robust linear model in R with MM weights using the rlm() in the MASS package. `R`` does not provide an $R^2$ value ...
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47 views

Can I use weights generated by robust regression in a quasipoisson glm in R?

I have response variable count data that should be treated as quasipoisson or something similar. This data also contains outliers which are important to the dataset. I cannot find an r package that ...
2
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1answer
62 views

Heteroskedasticly Consistent Estimators for Var-Cov Matrix, Large Sample OLS Regression

I have a cross-sectional data sample of nearly 40,000 observations and tests for heteroskedasticity fail to reject the assumption of homoskedasticity. However, it seems common practice to report ...
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1answer
64 views

Consistent, non-parametric, robust (to fat tails) estimation of expected value of an asymmetric distribution

Question: Is anyone aware of a consistent, non-parametric estimator of the expected value of an asymmetric distribution that is robust to fat tails? What if we constrain ourselves to the class of ...
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34 views

How to find Influence function?

Derive $IF(x;T,F)$ when $$\displaystyle T(F)=\int_{F^{-1}(\alpha)}^{F^{-1}(1-\alpha)}x ~dF(x)$$ Here $IF$ stands for Influence function. Trial: Here $$\begin{align}IF(x;T,F) &=\lim_{t\to ...
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5answers
479 views

What would a robust Bayesian model for estimating the scale of a roughly normal distribution be?

There exists a number of robust estimators of scale. A notable example is the median absolute deviation which relates to the standard deviation as $\sigma = \mathrm{MAD}\cdot1.4826$. In a Bayesian ...
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1answer
22 views

Repeat normality check after modifying group cut-off?

I have a set of data which consists of one independent variable (2 groups) and one dependent variable. I successfully checked for normality (each group separately) and conducted a t-test. Now I want ...
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2answers
73 views

What would be a parametric model with properties similar to the Theil-Sen estimator?

The Theil-Sen estimator is a really nifty algorithm that produces a regression line that is relatively insensitive to outliers both in the response variable and the predictor variable. I've been ...
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25 views

Iteratively reweighted least squares : asymmetric weights

For robust m-estimation, all the convergence results I'm aware of assume symmetric weights (eg: Huber function) in their formulation of the iterative reweighted least squares algorithm. Does the ...
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1answer
147 views

Quantile regression vs. Li's regression: which should I use, and when?

Is there a general rule of thumb about when robust regression or quantile regression is preferred in the presence of outliers? For example, I have a dataset where the DV exhibits extreme positive ...
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1answer
69 views

Robust test for time series count data

I'm going to analyse suicide rates for a time series, and I'd like to use robust tests, but I don't know which would be a good one. My purpose is to compare the variation of the suicide rates through ...
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31 views

Is there a method for testing follow-up individual factor and item invariance using the lava an or semTools packages in R?

I've found the "measurementInvariance" command from the semTools package EXTREMELY helpful recently, but now I am wondering if there is a way to conduct follow-up factor-level and item-level ...
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1answer
80 views

Inspecting assumption of homoscedasticity

Using a Fligner test to infer about the respect of the assumption of homoscedasticity is not very smart given that the Fligner test tests to the null that there is no difference of variance between ...
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1answer
113 views

Robust regression and Sandwich estimators

Can you give me an example of the use of sandwich estimators in order to perform a robust regression? I can see the example in ?sandwich but I don't quite ...
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1answer
866 views

Error “system is computationally singular” when running a glm

I'm using the robustbase package to run a glm estimation. However when I do it, I get the following error: ...
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1answer
69 views

Robustly standardize residuals in MM regression

Does anyone know how we can robustly standardize the residuals in MM regression? First we perform MM regression and then obtain the residuals: how can we robustly standardize the residuals obtained ...
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2answers
170 views

When is the median more affected by sampling error than the mean?

I'm writing a paper on making probability estimates, and it's been asserted to me that I should take the median of the estimates given by my participants, rather than the mean. I've been told I should ...
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25 views

What is the statistical efficiency of L-moments?

In particular I am interested in the scale estimator. Hopefully it is much better than that of IQR.
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13 views

F test for regressions with a small N with robust standard errors [duplicate]

I have a binary dummy with only a very small number of values for this dummy set to "1" (say 7 out of 120). When I run the regression the F-test using robust standard errors, the f-test does not show ...
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3answers
166 views

Mean has lower standard error than 5% trimmed mean?

I'm investigating using a trimmed mean to measure the location of various distributions. The distributions sometimes are heavily contaminated and sometimes not. Usually they follow something similar ...
4
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1answer
102 views

Does inference from a heteroskedasticity-consistent covariance matrix follow the t-distribution or the normal?

Background I'm currently looking into how reliable confidence intervals are on bounded scores (EQ-5D) and I compare regular asymptotic, robust and botstrap-based confidence intervals. The robust ...
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118 views
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74 views

How to use robust variance estimator in F-test

Please help me understand something: In a linear regression framework we test for linear hypothesis $H_0: R\beta-q=0$ using an F-test. Following Greene's "Econometrics Analysis" 7th edition page 118: ...
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1answer
480 views

Adjusted $R^2$ & F test are not shown in regression with robust standard errors in Stata

The adjusted $R^2$ is not shown when a regression with robust standard errors is calculated in Stata. This is surprising to me since the value of the $R^2$ is unaffected in regressions with robust ...
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116 views

Robust Residual standard error (in R)

I have a question regarding to the concept of robust standard errors. What I found about that topic is, that one can estimate the robust standard error for regression coefficients to eliminate ...
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0answers
357 views

F test and categorical variables

I am trying to compute a regression. I have a continuous dependent variable (investment in millions of dollars) One continuous independent variables Five dichotomous indicators (1 / 0) Four ...
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1answer
74 views

Sample variance Fisher consistency

I am reading conflicting references regarding the Fisher consistency of the sample variance. $$s^2 = \frac{\sum_i^n (x_i - \bar{x})^2}{n}$$ Could anyone explain me how to proof whether $s^2$ is ...
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3answers
134 views

Robust standardization of data

I have some data where I want to determine whether the shape of the probability distribution has changed compared to 10 years ago. One example is that I have for various automobiles multiple measures ...
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79 views

Robust estimation of mean with small sample size

Working with a 2D sensor. A row consists of 4096 samples, of which there are 16 reference samples (the rest are active). The reference samples do not measure the signal, but are used to estimate the ...
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53 views

Sample variance robustness

I am trying to understand the robustness of the sample variance. I want to calculate its influence function and in order to do so a previous step is to obtain the functional for the contaminated ...
2
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1answer
142 views

Alternative tests for Hotelling's two-sample T-test

I have a bunch of vectors from two groups, $X$ and $Y$, and each vector in either $X$ or $Y$ groups has $m$ elements. Now I have $X_{1},\ldots,X_{8}$ and $Y_{1}, \ldots, Y_{8}$ in each group, and ...
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2answers
118 views

Robust ANCOVA literature

I am looking for some source of information, some articles about Robust ANCOVA. Can you suggest me something? And do you know any source that directly gives information about how to perform various ...
2
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1answer
36 views

Estimate the parameters of an ellipse in the presence of large outliers

I have a number of points $x_1,\ldots,x_m\in\mathbb{R}^n$ with weights $w_1,\ldots,w_m$ between 0 and 1. There is an ellipse which contains a very high concentration of points with weights close to ...
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101 views

Post hoc tests for robust mixed design ANOVA using R

Is it possible to compute the function mcp2atm with unequal sample size? I ran the robust Mixed Design ANOVA by using tsplit and ...
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1answer
427 views

Investigating robustness of logistic regression against violation of linearity of logit

I am conducting a logistic regression with a binary outcome (start and not start). My mix of predictors are all either continuous or dichotomous variables. Using the Box-Tidwell approach, one of my ...
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2answers
228 views

Hypothesis testing a location shift in heteroscedastic and non-normal data

How do I test for a "location shift" in something like the mean or median if the shape of the distribution has changed quite significantly between groups? Often an experimental intervention seems to ...
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1answer
119 views

Skewness in residuals

I have skewness of -0.5 in the residuals which does not seem to be improve much after using logs/root. Is this a major concern? Tests relating to homoskedasticity, multicollinearity, outliers all ...
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56 views

Robust GAM that covers Gaussian distribution

I was looking at CrossValidate archives as well as r-archives and crantastic...for a package that has a robust approach to generalized additive models. I found two packages "robustgam" and "rgam" but ...