Questions tagged [m-estimation]

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Robust regression with M-estimators

I have a couple of question regarding robust regression with M-estimators, such as Huber estimator or Tukey biweight estimator: Is it possible/common to combine these with regularization terms, such ...
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0answers
12 views

Why does the computational time of maximum likelihood estimators depend only on the number of UNIQUE observations?

The following paper says that the computational time of least squares, maximum likelihood, and M-estimators in general depend only on the number of UNIQUE observations. Intuitively it makes sense to ...
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2answers
143 views

$\sqrt{n}$-equivalence of M-estimator based on plug-in estimator

Suppose our model has a nuisance parameter $\eta_0$ of which we possess a consistent estimator $\hat{\eta}_0$. We obtain an estimator $\hat{\theta}$ of a parameter of interests $\theta$ by finding ...
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2answers
174 views

$\sqrt{n}$-consistency of M-estimator based on plug-in estimator

Note: This is a follow-up on a previous question that was concerned about consistency, but this time seeking $\sqrt{n}$-consistency. Suppose we estimate a quantity $\theta_0$ by the $\tilde{\theta} = ...
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1answer
167 views

Consistency of M-estimator based on plug-in estimator?

Suppose we estimate a quantity $\theta_0$ by the $\tilde{\theta} = \hat{\theta}(\eta)$ that solves the estimating equation $$S_n(\tilde{\theta}, \eta_0) = 0$$ where $\eta_0$ is a nuisance ...
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0answers
27 views

Hypothesis testing - OLS v M-estimation

I am trying to determine if two regression estimates are different. The first is obtained by ordinary least squares (OLS) and the second is obtained by M-estimation. As a minimum example, fits for ...
2
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1answer
79 views

Regression model with some regressors depending on other regressors

We want to investigate which variables determine the final grade in a University exam (say Y_2), which can assume integer values between 18 and 32. We think that Y_2 depends on: 1) Personal variables ...
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2answers
169 views

M-estimation for regression

An M-estimator $(\beta,\sigma)$ is defined as the parameters that minimize $$ \displaystyle \sum_{i=1}^n \rho\left(\dfrac{y_i -x_i^T \beta}{\sigma}\right)$$, for some robust function $\rho$. I ...
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0answers
193 views

M-Estimation General Idea

I am having trouble understanding some of the ideas behind $M$-estimation and it would be great if someone could help me out. From my understanding, it just an estimate that comes out of minimizing $\...
4
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1answer
199 views

How to implement the sandwich estimator in a semi-parametric situation?

I am trying to implement a sandwich estimator described in Zhang et al. (2012, p. 1012) in very brief terms. The information they give is not enough for me to understand what has been actually done, ...
5
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1answer
235 views

Is every L-estimator an M-estimator?

This is a follow-up to this question: Do M-estimators and L-estimators overlap?. In particular, the answers to that question suggest that there are L-estimators which are not M-estimators, but do not ...
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0answers
672 views

Simulate different types of outliers (with R) in a linear regression?

I'm trying to simulate a regression model with outliers to implement and understand more deeply the robust regression. I tried using a mixture between normal errors and uniforms.But as you can see, ...
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0answers
62 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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0answers
669 views

Use linear regression to detect outliers and leverage points

I want to use linear regression to pre-process the data (e.g find outliers) so that I can use techniques like ANOVA to analyze the data. The goal is not to fit a regression model. I saw two posts ...