Questions tagged [method-of-moments]

A method of parameter estimation by equating sample and population moments then solving the equations for the unknown parameters.

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Using the Yule-Walker equation to calibrate an autoregressive model with the method of moments

Consider the following discrete autoregressive $\epsilon_t$, where $\epsilon_t \in (\pm 1 ) \forall \ t \geq 1$. We think of $\epsilon_t$ as the child of a previous sign at time $t-l$, where $l$ is ...
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Method of moments estimator for a probability of an event

I need to find the method of moments estimator for $P(pois(\lambda)=0)$. I already worked out the MME $\hat{\lambda}=\bar{X}$ but I'm not sure how to proceed here because I can only see how this ...
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When is the Optimal weighting matrix in GMM singular?

currently I am trying to estimate a simple linear regression: $$y_t = X \beta + \varepsilon_t,$$ where I try to find 4 coefficients and one specific predictor is an ...
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Is this correct for (generalised) method of moments?

I am reviewing a MOOC and realised... I didn't grasp the method of moments, so I did try to get it back "from scratch". Are the above equations/sentences correct ? In the MOOC the analysis ...
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How does the information in the problem statement and this solution align with the provided description of the method of moments?

I have the following problem: Let $Y_1, Y_2, \dots, Y_n$ be i.i.d. $\text{Uniform}(\theta, 1)$ random variables, and let an estimator be $\hat{\theta} = \min\{ Y_1, Y_2, \dots, Y_n \}$. You may find ...
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Negative-Binomial Method of moments with an offset

Given the method-of-moments approach to estimate the parameters of the NB-2 distribution $\mu$ and $\phi$: $$\mu = \bar{y}$$ $$\phi = \frac{\bar{y}^2}{s^2 -\bar{y}}$$ How can this be extended to ...
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Which estimator is preferred for a random sample from $P_\theta(X=x)=\theta^x(1-\theta)^{1-x}, x=0,1; 0 \le \theta \le \frac{1}{2}$?

Let $X_1,\cdots,X_n$ be an i.i.d sample from $P_\theta(X=x)=\theta^x(1-\theta)^{1-x}, x=0,1; 0 \le \theta \le \frac{1}{2}$. Its the method of moments estimator of the MLE better? Why? My work: I ...
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Intuition behind Method of Moments estimators of Binomial distribution

The method of moments estimators of the binomial distributions ($x \sim Binom(n, p)$) are a bit weird... I got $\hat p = \bar x + 1 - \frac{\sum x_i^2}{\sum x_i}$ and $\hat n = \frac{\bar x}{\hat p}$. ...
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How to estimate parameter using yule-walker/method of moments?

Suppose you observe the first T periods. X1, X2, · · · , XT of an AR(1) process Xt = µ + φXt−1 + et. Derive the Yule-Walker/Method of Moment estimate φˆMM for φ. I thought YW was used to solve for ...
Method of moments estimator, $P_\theta(X = x) = \frac{1}{\theta}$
I am struggling with finding a method of moments estimator for (seemingly) simple situation: pdf is given by $P_\theta(X = x) = \frac{1}{\theta}$, $x \in$ {1,2,...$\theta$}, where $\theta \in N$. My ...