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Questions tagged [quasi-maximum-likelihood]

Quasi-maximum likelihood estimator (QMLE), a.k.a. pseudo MLE, is a replacement of MLE maximizing a function that is related to the likelihood function, but with some parts potentially misspecified.

Quasi-maximum likelihood estimator (QMLE), a.k.a. pseudo MLE is a parameter estimator maximizing a function that is related to the likelihood function, but with some parts potentially misspecified. QMLE was proposed by Wedderburn (1974) as a replacement of MLE and is attractive for its simplicity. Under some assumptions, QMLE is consistent and asymptotically normal, but it is less efficient than the MLE. A couple of good intuitive explanations of QMLE are offered in the thread "Idea and intuition behind quasi maximum likelihood estimation (QMLE)".

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Idea and intuition behind quasi maximum likelihood estimation (QMLE)

Question(s): What is the idea and intuition behind quasi maximum likelihood estimation (QMLE; also known as pseudo maximum likelihood estimation, PMLE)? What makes the estimator work when the actual error distribution does not match the assumed…
Richard Hardy
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Fixed-effects Poisson estimator using quasi-maximum likelihood

I am trying to run a fixed-effects Poisson Quasi Maximum Likelihood estimator on 3-dimensional(year, country, industry) Panel data. The dependent variable is the number of patents(non-negative and non-integer) and the main independent variable is…
Laura
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QMLE with normal distribution for GARCH - consistent & asymptoticaly normal? (R, fGarch)

In the section Details of the documentation of the garchFit function we find the following statemement: "QMLE stands for Quasi-Maximum Likelihood Estimation, which assumes normal distribution and uses robust standard errors for inference." But in…
Archimede
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Estimating the asymptotic distribution of a quasi maximum likelihood estimator

We consider the following GARCH(1, 1) model: $y_t = h_t \epsilon_t$ where $(\epsilon_t)_{t \in \{1, \dots, n\}}$ are i.i.d. random variables with mean 0 and standard deviation 1. $h_t = \omega + \alpha \epsilon_{t-1}^2 + \beta h_{t-1}^2$ A standard…
Thomas
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GEE, quasi-likelihood and what it generalizes

Wikipedia formulates Generalized Estimating Equations (GEE) as Given a mean model, $\mu_{ij}$, and variance structure, $V_{i}$, the estimating equation is formed via: $$ U(\beta) = \sum_{i=1}^N \frac{\partial \mu_{ij}}{\partial \beta_k}…
Tim
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purpose of using quasi likelihood

Based on MLE (Maximum Likelihood Estimator), we knew that the puprose is to maximize the likelihood function. Then how about quasi likelihood ? Is quasi likelihood just modelling between mean and variance ?
Izzati
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What exactly is a quasi-likelihood model?

I tried reading Wedderburn (1974) http://matt-wand.utsacademics.info/webStatSem/Wedderburn.pdf but I'm not wrapping my head around exactly what quasi-likelihood model is, in particular with generalized estimating equations. I understand that GEE…
EJ16
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Maximum likelihood estimation when the model is misspecified (and the true data generating process is a mixture model)

I'm interested in the properties of maximum likelihood estimators under a particular form of model misspecification: We observe data $\left\{X_i\right\}$ generated from a finite mixture model Let $\pi_k$ denote the mixture weight for component $k$,…
Adrian
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Quasi-Poisson Regression with non-integer count data

I am trying to run a fixed-effects Poisson Quasi Maximum Likelihood estimator on 3-dimensional(year, country, industry) unbalanced Panel data. The dependent variable is the number of patents(non-negative and non-integer). The patent data is…
Laura
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How to make optimization work normal in GARCH estimation, and question on standard errors?

I am currently trying to implement GARCH-M (garch in mean) model in Python (cannot use existing packages, and just want to understand the ground). I wanted to write not a big (but enough) piece of code for this purpose. I wrote the class, but I have…
Krainev Konstantin
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What are the regularity conditions for quasi-maximum likelihood estimators?

What are the regularity conditions for Quasi-Maximum Likelihood Estimators (QMLE)?1 Could you advise me a good book where I can find detailed proofs? 1. For example, regularity conditions for MLE are discussed here (pdf).
user216418
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How to compute sandwich estimator with QMLE and Poisson regression in R (using glmrob package)

I am trying to applying a sandwich estimator to a Poisson regression with QMLE in R, where I used the glmrob function. The code I am using looks like: model <- glmrob(y ~ x + x1 + x2, family = poisson, data = data, method= "Mqle", control =…
Daniel M
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Quasi-likelihood and matrix dimension

Quasi-likelihood estimating equations (quasi-score function) for the estimation is as follows $$\sum_i\frac{\partial{\mu_i^{'}}}{\partial{\beta}}V_i^{-1}(y_i-\mu_i)=0.$$ The $\frac{\partial{\mu_i^{'}}}{\partial{\beta}}=X_{n,p+1}$ matrix. The extra…
Lila Pfeiffer
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Quasi-likelihood can't be generated by any valid probability distribution

I am learning about quasi-Poisson and i'm stuck at the concept of quasi-likelihood function. In wikipedia, it is said that: The term quasi-likelihood function was introduced by Robert Wedderburn in 1974 to describe a function that has similar…
InTheSearchForKnowledge
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QMLE (conditional density model posed incorrectly)

I need clarification on which is the correct way of stating the problem. Let the collection of pairs $\{(x_i,y_i)\}_{i=1}^n$ be a random sample for a pair $(y; x)$ where $y>0$ and $x$ contains one, that satisfies the conditional density model…
Maybeline Lee
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