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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How does Huber compute the $\operatorname{var}(s_n)/E[s_n]^2$ and $\operatorname{var}(d_n)/E[d_n]^2$?
(N.B. I am cross posting this question from math stackexchange since after
x days I have still not received any responses.)
How does Huber in book 'Robust statistical procedures' in chapter 1 compute ...
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Interpet coefficient estimates with log(Y) in rdrobust package
1.I want to interpet the coefficients of RDD model above. The dependent variable is log-transformed. Should it be the same as linear regression even though I am using local polynomial regression with ...
LearningR
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How to implement an S-estimator
I'm trying to implement an MM-estimator in python. I have a working implementation of an M-estimator statsmodels.RLM - which is implemented as an iteratively re-weighted least squares algorithm. I am ...
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Effect of robust maximum likelihood estimator in structural equation modelling when data is normal?
I understand that when data are nonnormal robust maximum likelihood estimator can be used.
I'm wondering are there any disadvantages of using a robust maximum likelihood estimator when the data are ...
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Structural equation modeling (latent growth models): robust estimators to handle outliers?
Can I use robust estimators (e.g., "MLM" and "MLR"estimator lavaan options) to overcome outliers within my sample, or should I remove outliers?
For context, I am modelling the ...
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How are robust standard errors applied in logistic regression
I have been reading up on robust standard errors and had a few questions regarding how their use in logistic regression.
I have read here that heteroscedasticity is not an issue in logistic regression ...
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Robustness check in Structural Equation Modelling (SEM) in R
I have conducted SEM analysis in R and used Maximum Likelihood Robust estimator as my data are categorical and deviate from multivariate normality. when I submitted my manuscript, one reviewer asked ...
Bahar
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Influence function of the IQR
In class I am told the influence function of the IQR should be a constant times the difference between the influence function for the 75th percentile and the influence function for the 25th percentile,...
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How do you use ordinal response data with several random effects to do robust hypothesis testing?
I want to explore the roles of lung presence and habitat on tadpoles' ability to tolerate low oxygen levels. My experimental design generated several measurements of "responsiveness" (on an ...
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Outlier detection for observations with sinusoidal relationship, incomplete information
I was looking for recommendations for an outlier rejection problem I find myself needing to solve.
I have a set of measurements (12 at a time) which vary sinusoidally according to
$$
d = \begin{...
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Model comparsion for robust linear mixed models (robustlmm)
I'm currently working on a project where I've fitted 4 robust linear mixed models. However, I've hit a bit of a roadblock when it comes to model selection. I've been using the AIC (Akaike Information ...
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Anova violates normality assumption for error data
I have a 2 x 2 repeated measures ANOVA (N = 51) with Error Rate data as the dependent measure. The error data violates the normality assumption, even when outliers are removed. I have looked at the ...
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Robustness of Mann Whitney U Test for partially paired data
I'm curious if anyone is aware of a publication that addresses the following matter or could provide a mathematically or reasonable response to the following question:
In a pre-post study where ...
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Reconciling Nondeterministic and Probabilistic Decision Rules
I've been getting a bit stuck recently on how to reconcile the two seemingly-competing ideas of nondeterministic and probabilistic decision rules.
As an example:
Let $t=0$ denote the current time and ...
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Mediation model with non-normal data
I want to conduct a mediational analyses with three variables:
Predictor: it is the result of a memory test with range -1 to 1.
Mediator: it is the absolute error made by the participant when ...
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Is this algorithm for robust estimation of the covariance matrix sensible?
I have a high dimensional dataset $\bf{X} \subset \mathbb{R}^d$, which is multimodal and has outliers. I want to estimate a robust measure of association, something like the correlation between two ...
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Modeling outliers in maximum likelihood estimation with gradient descent
Consider a set of 3D points $X = \{x_1, x_2, ...x_n\} $ with $ x_i\in\mathbb{R}^3$ on which we want to fit an arbitrary probability distribution. The distribution we want to fit models some ...
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pros and cons of different robust measures of scale/ dispersion
I would very much appreciate some help regarding how to interpret different robust measures of scale (Inter-quartile range or IQR, biweight midvariance, and median absolute deviation or MAD). Thus, ...
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Is truncated mean a biased estimator
We have data $X_1, \dots, X_n$ which are i.i.d copies of $X$. Where we denote $\mathbb{E}[X] = \mu$, and $X$ has finite variance.
We define the truncated sample mean:
$\begin{align}
\hat{\mu}^{\...
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How to check for multicollinearity in Poisson regression model with robust error variance
I have created a Poisson regression model with robust error variance (https://academic.oup.com/aje/article/159/7/702/71883) to calculate relative risks.
This is the Poisson regression model:
...
Laura Omann
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Adjust the "Threshold" in a robust regression
I am trying to perform a robust regressions using the lmrob function in R.
I am getting this error Message:
...
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Robust regression (Passing-Pablok) with more than 50% of the points on the coordinate(0,0)
I have an issue with a regression problem. Indeed, I need to fit a linear regression on this data. The problem is more than 50% of the data points are located in the origin (0,0) of the graph (because ...
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Proving upper bound for truncated difference
Let $X$ and $Y$ be real valued random variables. And define a truncation operator as:
$\begin{align}
X(\tau) = (|X| \wedge \tau) \; \text{sign}(X), \quad \tau > 0
\end{align}$
Now, I am not ...
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Is Centering Data Around Their Medians in Least Absolute Deviation Regression Model (No Intercept), a Good Robust Practice For Smaller Data Sets?
Per the regression model:
$\mathbf{y} = f(\mathbf{x},\mathbf{\beta}) + \mathbf{\epsilon}$
Where the $\beta$ estimate of LAD regression is given by:
$ \hat{\beta}_{LAD} = \text{argmin}_{ b} \sum_{i=1}^...
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How to determine if my model is robust? Should the coefficients be same?
I want to run robustness tests for my model. For example, by reducing the sample to heavily concentrated groups, running a different regression (probit etc) etc. But, how do I ascertain that my ...
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Proving upper bound for Bias of truncated sample mean
We have data $X_1, \dots, X_n$ which are i.i.d copies of $X$. Where we denote $\mathbb{E}[X] = \mu$, and $X$ has finite variance.
We define the truncated sample mean:
$\begin{align}
\hat{\mu}^{\...
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Robust ANOVA using the WRS2 Package: One way repeated measures of ANOVA [closed]
I'm unable to use the rmanova function in the WRS 2 package that computes a one-way repeated measures ANOVA (see page 25).
...
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When can I ignore endogeneity problem?
Technically, endogeneity occurs when a predictor variable (x) in a
regression model is correlated with the error term (e) in the model.
This can occur under a variety of conditions, but two cases are
...
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Robustification in lavaan: Difference between M, MV and MVS?
In lavaan, I am running a two-factor CFA on a questionnaire with 28 items, all of which are scored on a 6-point Likert scale. In total I have ~350 participants who completed the questionnaire.
Because ...
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robust linear mixed model(rlmer): how to unpack the three-way interaction
I found a three-way interaction effect (each of the three factors has two levels) during a robust linear mixed model(RLMM). I'm wondering how to unpack this interaction.
What I had done is: first ...
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Mean of bootstrapped medians
I have a large set (10^6) of very small sets (5-10 entries) of numbers. For each of them, I want to compute a sensible average measure. An example might be this:
$$
x = [-2, 5, -1, 3, 100]
$$
Because ...
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Model selection for robust linear regression methods
I have fitted respectively a zero-knot, a one-knot and a two-knot linear spline to my data, and I need some index of model performance for model selection. The crucial point is that the splines are ...
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Intuitive understanding of influence function
This question asks about influence functions. Probabilityislogic's answer is a bit fuzzy to me, but I can make more sense of jayk's answer, as this was the way influence function was presented to me ...
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Robustness of Posterior distribution wrt likelihood function
Suppose we have
$$
X_1, \ldots, X_n \mid \theta \, \mathop{\sim}^{iid} \, L(\cdot \mid \theta), \quad \theta \sim \pi
$$
By Bayes' theorem, the corresponding posterior distribution is
$$
\pi_n(\mathrm ...
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How can I estimate robust standard errors for robust estimators? R
I am doing a robust regression and I want to estimate robust standard errors for my regression. I do know how to do a robust regression in R and how to estimate a robust standard errors for a ...
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How do the "C" step and robust weighting work in the FASTMCD algorithm for robust covariance estimation?
I am reading up on the FastMCD algorithm [https://arxiv.org/pdf/1709.07045.pdf#page=2] hoping to better understand its implemenation. I think I follow the high level concept for MCD
Its basically the ...
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Robust estimators for count data
I am looking for robust estimators for parameters of a processes producing count data:
$$
(n_1,...,n_K), n_i\in\mathbb{N}
$$
that is the underlying distribution is something like Poisson or Negative ...
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Robust Optimization: Minimizing $\mathbb{E}[X]+\alpha\sigma(X)$ vs. $\mathbb{E}[X]+\alpha\textbf{Var}(X)$
In robust optimization it is common to minimize the objecive $\mathbb{E}[X]+\alpha\sigma(X)$ instead of the expectation. Would it also be sensible to minimize $\mathbb{E}[X]+\alpha\textbf{Var}(X)$ ...
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Robustness of Quantile Regression
Is the 99th Quantile Regression model a robust model?
From my understanding, Quantile Regression is supposed to be robust in nature, but removing some outliers using IQR, the results obtained by 99th ...
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Distributionally Robust Optimization: how to know distributions in ambiguity set?
In distributionally robust optimization, it is said that ambiguity sets are created from empirical sample distribution such that the distributions within the ambiguity set 'Q' are at certain ...
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Logistic regression via robust glm (glmrob) not appropriate if have only one observation in one of two categories of an independent variable?
I received abnormal results when using glmrob (R function from robustbase) when assessing the association of a binomial independent variable X0 with a binomial dependent variable Y using logistic ...
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Robust options to fit GLM or GAM for overdispersed Poisson counts (quasipoisson or negative binomial) in R
It appears glmrob from the robustbase library does not support quasipoisson or ...
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Error in solve.default(pdMatrix(a, factor = TRUE)) : system is computationally singular: reciprocal condition number
I am performing a linear mixed-effect model.
...
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Robust Beta Regression in R
I have been trying to fit a beta regression to a percentage/proportion outcome variable. I used libraries as glmmTMB, gamlss, ...
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With what goodness measures can cross-validation be done for robust regressions?
Cross-validation involves splitting data in training and test sets (several times) and assessing the goodness of applying the fitted coefficients from the training set to the test set. I was wondering ...
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How to use the bwwtrim function of the WRS package? (robust 3-way mixed ANOVA)
in our study, we look at the effects of typical/enhanced body checking on eating pathology before and after the intervention, depending on the level of body concern (see below). Since the assumptions ...
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Do I need to test for autocorrelation or normality assumption if I am running the regression with standard errors?
I used OLS regression to estimate a relationship between X and Y with a couple of control variables. However, when I tested for heteroskedasticity with Breusch–Pagan/Cook–Weisberg test, my residuals ...
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how well would a robust mixed model fit these data? R (rlmer)
I want to investigate Y ~ X1 * X2 + (1|ID on this dataset (there's a plot of these data in that post too, it's the same dataframe)
Y is a continuos outcome ...
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How do Measure "Robustness" in Statistics?
I am an MBA Student taking courses in Statistics.
Our prof was comparing two different methods of estimating the parameters for a regression model: General Method of Moments (GMM) and Maximum ...
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Are moments more robust than MLE?
I am an MBA Student taking courses in Statistics.
We are learning about different ways to estimate the parameters (i.e. coefficients) of a Regression Model. Our professor indicated that there are two ...