Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [m-estimation]

20 questions
8
votes
1 answer

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 parameter that is known. Suppose that the assumptions of…
Guillaume F.
  • 696
  • 3
  • 11
6
votes
2 answers

$\sqrt{n}$-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 the $\theta$ that solves the estimating…
Guillaume F.
  • 696
  • 3
  • 11
6
votes
1 answer

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 give such an example. More concretely, suppose I…
Asterix
  • 339
  • 1
  • 7
4
votes
1 answer

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, which is why I re-produce the problem here in…
tomka
  • 5,874
  • 3
  • 30
  • 71
3
votes
0 answers

Why there are three functions for robust M-Estimators

I have spent a lot of time reading about Robust regression, especially M- estimators and their related functions (objective function, score function, and weight function). I know that M-estimators have high relative efficiency and low breakdown…
Peter Smith
  • 309
  • 2
  • 8
3
votes
2 answers

$\sqrt{n}$-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 $\tilde{\theta} = \hat{\theta}(\eta_0)$ that solves the estimating…
Guillaume F.
  • 696
  • 3
  • 11
3
votes
1 answer

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, the estimates do not suffer large variations. I…
Héctor Garrido
  • 111
  • 15
2
votes
1 answer

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 related to the student: sex, family, income,…
grames
  • 121
  • 3
2
votes
0 answers

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 $\sum{\rho(r_i)}$ for some arbitrary function…
user153009
  • 255
  • 2
  • 5
2
votes
0 answers

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 normal for least squares models. Is it also true for…
user251385
  • 63
  • 6
2
votes
1 answer

M-estimators: textbook examples

I would like to practice with solving M-estimators problems, but I cannot find where they are easily explained. Could you please recommend me something?
user2575760
  • 441
  • 4
  • 15
1
vote
0 answers

M-estimator: There is no "of something" in the definition

I see that when talking about estimator, we have "of something", where "something" refers to a fixed parameter. For example, we say that the sample mean is an estimator of the population mean (a fixed parameter), or the sample variance is an…
TrungDung
  • 749
  • 4
  • 13
1
vote
0 answers

Invertibility step in proof of asymptotic normality of M-estimators

I am looking at a certain proof of asymptotic normality of M-estimators and there is a matrix $V$ which is known to be invertible anda random variable $X_n = V + o_p(1)$ (that is, the difference converges to zero in probability as $n \to \infty$). I…
I_cosine_this
  • 11
  • 2
1
vote
0 answers

M estimation for independent but not identical random variables

I am looking for advanced theories for M estimation. Suppose $X_1,\dots,X_n$ comes from some parametric family. They are independent but not identical with one common parameter $\theta$ and one own parameter $a_i$(not same for all cases). I am only…
user693607
  • 11
  • 1
1
vote
1 answer

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 as those used in ridge and lasso…
Roger Vadim
  • 1,481
  • 6
  • 17
1
2