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

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Robust methods and penalized regression

Are penalized regression methods such as ridge or lasso sensitive to outliers? If so, what options are there in regards to robust methods for penalized regressions and are there any packages in R?
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15 views

Heteroskedasticity consistent SEs with Proc ROBUSTREG in SAS

We are using the Proc ROBUSTREG command in SAS to down-weight the influence of the outliers (mainly in the Y-direction). Furthermore, we wish to use heteroskedasticity consistent SEs and standardized ...
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29 views

PROC ROBUSTREG or PROC NLMIXED in SAS, to down-weight effects of non-normality and outliers

We are conducting an OLS regression in SAS. We have performed all diagnostic tests and concluded that there is non-normality in the residuals, influential outliers and heteroskedasticity. We would now ...
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2answers
68 views

Best regression correcting for non-normality, outliers and heteroskedasticity

We are performing a regression on cross-sectional data for $Y$ = subjective well-being (scale 0-10) and $X$ = working hours (divided into 5 dummy categories; less than 27 hours, 27-32 hours etc). ...
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1answer
44 views

Generating random samples from Huber density

Huber density, connected to Huber loss, can be defined as: $$ f(x) = \frac{1-\epsilon}{\sqrt{2\pi}} e^{-\rho_k(x)} $$ where $$ \rho_k(x) = \begin{cases} \frac{1}{2} x^2 & |x|\le k ...
3
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0answers
30 views

Is M-estimation valid only for regression models?

Is M-estimation valid only for regression models or does it's working hold good for robust estimation of parameters in other statistical models? I understand that M-estimators are asymptotically ...
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2answers
102 views

Robustness of correlation test to non-normality

I'm trying to reconcile two seemingly opposite statements about robustness to non-normality of the Pearson's correlation test statistic (where the null means "no correlation"). This CV answer says: ...
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23 views

Two more questions about Count Data

I almost became an opponent of the transformation of count data. (quite famous reference). But I still did not find answers to some important questions about non-transformed count data (I consider ...
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0answers
15 views

Robustness criterion (1978)

I am referring to bradley's journal relating to the robustness criterion. According to his liberal criterion, the simulated type 1 error rate have to between 0.5 alpha < p < 1.5 alpha. since i ...
0
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1answer
127 views

p values and significance in RLM (MASS package) R

I'm running some regression analyses and got pretty confused about R's output when it comes to robust regression models. When I run a OLS -- using the command ...
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0answers
25 views

Influence function of OLS to check the robustness

I understand what is the influence function. I'm just blocked on this exercise. We consider the regression following. $y_i = x_i^T \beta + \epsilon_i$ Can somebody help me to calculate the influence ...
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18 views

I can't correct the OLS model with heteroskedasticity by the lmtest means

i'm using a selvaggio model to explain the behavior of deposits in a bank's data, and i need to use the estimated parameters, the problem is the heteroskedasticity that i detectect with breusch-pagan ...
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21 views

Robust Estimation of Negative Binomial: Help in understanding the code

I would like to understand following R code. Robust methods used here works, I understood it, but sometimes too many options for choice is not a good thing - now I am confused which method should I ...
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24 views

Robust Bootstrap Covariance Estimator

I sometimes see particular bootstrap repetitions give "wild" regression coefficient estimates for one or more bootstrap resamples. This occurs more often in binary logistic regression. One or two ...
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0answers
49 views

Questions about negative binomial distribution

1) I know that my data is NB distributed. But also I know that it has several outliers (probably, zeros and extremely big numbers). How can I estimate NB? I found the trick answered here, on CV site, ...
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0answers
25 views

Inter-quartile range

If we have a non-normal distribution say (Weibull) and we used a robust estimator of standard deviation in term of inter-quartile range (IQR). Is it possible we replace IQR=3*SD?
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33 views

$r^2$ using Robust Regression

I am interested in measure of quality of robust regression. How should I calculate it? It is clear that $r^2$ of robust regression should be smaller than $r^2$ OLS regression. Even if OLS is totally ...
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0answers
8 views

how does the Qn estimator work

I was given a short introduction to alternative robust methods to the MAD used in statistics, one of them being the Qn estimator. This one is denoted as: \begin{equation} Q_n = d( |(x_i - x_j)|:i<j ...
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40 views

alternative to IQR

I am currently making a short literature study on robust and efficient estimators. Some very well known are the median absolute deviation (MAD) and the interquartile range(IQR). However they both have ...
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27 views

Is there an R function for calculating a scale M-estimator based on Tukey's bisquare rho function? [closed]

The bisquare function is the second example in this wikipedia page https://en.wikipedia.org/wiki/Redescending_M-estimator#Examples
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27 views

Interpretation of drop.test output in R

Could someone clarify the purpose of the drop in dispersion test (drop.test) in the Rfit package in R? I think that it shows the difference in explanatory power ...
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0answers
15 views

Deleting outliers in (almost) uniform graph

I wrote an algorithm that finds the centroids of rectangles which are on the same line and groups these rectangles together. I know that only those rectangles with a roughly equal size belong ...
3
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0answers
28 views

Rules of thumb for a proportion of outliers depending on the dimension

I am implementing and benchmarking different "robust" PCA (principal component analysis, see for instance Robust Principal Component Analysis?) for data that should align (I have no prior on the ...
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1answer
26 views

When to use robust methods and how to report them in a paper?

Wilcox in his package WRS in R software managed to provide easily accessible robust techniques to conduct usual hypothesis testing like t-test, ANOVA etc. I've ...
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27 views

robust estimator when $\mu/\sigma$ is constant

I have a large set of measurements consisting each of about 100 points, (normally distributed), with up to 20% outliers. The outliers are all shifted towards positive values. From the physics, I know ...
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1answer
53 views

Robust correlation in python? [closed]

Is some kind of robust (especially to outliers) correlation methods easily available in python? I have a suspicion that outliers might be causing false positives in my data.
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50 views
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71 views

How to choose t-distribution degrees of freedom in “robust” Bayesian linear models

It is well known that in both frequentist and Bayesian linear models, outliers can greatly influence the parameter estimates. Consider the simple example where one outcome variable, $y$, is predicted ...
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50 views

confidence intervals for cox proportional hazards with 0 events in one treatment arm

We are performing a multivariate cox proportional hazards analysis with 6 covariates. Two of the covariates (Pre_ASCT_response2 and NGS_graft_MRD2) are binary covariates with 0 events in one ...
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23 views

Inflated Type 1 error in glmer (for main effect but not interaction?)

I am doing simulations of type 1 error, power, and power' (power corrected for anti conservativity) for research on a specific application of (g)lmer, namely to small-N designs of longitudinal ...
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26 views

Should I check control variables for robustness?

I am working with count data and using a negative binomial regression. I have 3 core independent variables and control variables (age,education and sex). But the problem is that I have 8 age groups ...
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17 views

how can I calculate type one error rate?

how can I calculate type one error rate ? my study on robust estimators I search for calculating type one error to compare I found several article for that but no one explain how
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46 views

Fixed effects robust X random effects

I'm new to econometrics and Stata and I need some help. I'm trying to estimate a panel data model and I'm would like how to compare a robust fixed effects and a random effects model in Stata. I'm ...
0
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0answers
18 views

Correlation robust to outliers

I am concerned with Pearson correlation. My idea is to throw away the outliers in terms of absolute value, as it seems appropriate to my case. However, I don't know if I should do it only according to ...
0
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1answer
70 views

Correlation values aren't significant but the coefficients of regression are

I ran a regression model between X and y. I used robust regression. The results are significant, but when I ran a Pearson correlation I found that the correlation values aren't significant. I don't ...
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51 views

How to check the number of outliers in my data?

I have multivariate data and want to check for outliers. I guess there are both outliers in the predictor variables and the dependent variable. My idea was to fit robust regression methods after ...
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0answers
71 views

Robust regression and singular error

I got this error message from a robust regression in r ; "'x' is singular: singular fits are not implemented in 'rlm'" I could solve it by removing some variables. My question is , can i progrom r ...
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0answers
37 views

Feature selection for linear regression using bootstrapped RMSE as criteria

I'm trying to build robust linear regression model (lmrob from robustbase) using several (< 15) features. I know that traditional stepwise algorithms aren't the best alternative since they are ...
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0answers
23 views

A robust version of AIC using S-estimators

Again a special question concerning a paper about robust versions of the AIC: Robust versions of AIC. I am trying to implement the AIC.S criterion described on page 7. This should be no problem ...
3
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1answer
92 views

Huber loss prior in Bayesian context

Gaussian prior in Bayesian setting is equivalent to minimizing squared error, while Laplace prior minimizes the absolute error and leads to lasso regression. What (if any) prior distribution can be ...
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30 views

AIC for S-estimation: A robust version of the AIC

I have got a very special question according an interesting paper about robust versions of the AIC. You find the paper here: Robust AIC In the paper there are a few modified robust criterions ...
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132 views

AIC or BIC for robust regression?

I want to fit a robust regression method to my data because there are some outliers that might influence the estimates too much. Now my question: Are criterions like AIC or BIC still useful for robust ...
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1answer
88 views

Forward selection with BIC for robust regression methods?

I want to fit a robust linear model to my data using the rlm function in R. Is there any function that provides forward model ...
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0answers
16 views

Theil–Sen estimator in R with more than one variable? [duplicate]

Can Theil-Sen be defined for multiple linear regression? If so, is there an implementation in R for it? I simply want a formula a~b+c, but the package ...
3
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1answer
63 views

How to decide on Theil-Sen outliers?

After using the Theil-Sen estimator to obtain a robust linear regression (in my case 2D), I would like to decide on a set of outlier points. Is there a natural way to do this given the Theil-Sen ...
5
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1answer
215 views

why does R rlm {MASS} return different coefficients almost each time it is called?

I'm noticed that the rlm {MASS} returns almost every time different coefficients, even though I'm using the same parameters and the same data set I'm calling: ...
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22 views

Obtaining estimates and SE/CIs for a robust mixed design ANOVA

I have a two-way mixed design ANOVA with one between groups factor with two levels and one within groups factor with three levels. I have used robust methods outlined by Wilcox as my data was not ...
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1answer
64 views

Understanding a proof

The following is a proof of the existence of M-estimates from the book of Maronna et al. "Robust Statistics". While I understand their strategy, I am having trouble comprehending a step on their ...
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0answers
93 views

Robustness Weights in LOESS behaving strangely

I've been playing around with writing my own LOESS module in Python (2 reasons: first, I wanted the practice, and second, the implementation in statsmodels doesn't ...
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74 views

Presence of Heteroskedasticity, Robust Standard Errors - Stata

I have a panel of 49 observations, 7 countries, 7 years, running Panel fixed effects and IV fixed effects on Stata. I have used the modified Wald test to test for the presence of heteroskedasticity p ...