# 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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### 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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### Variance of the method of moments estimator for $\mu$ of log-normal distribution

Suppose the data has originated from a log-normal distribution with parameters $\mu$ and $\sigma$ (i.e. the mean and standard deviation of the underlying normal distribution). I have only the sample ...
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### Relation between OLS, MM and ML

What is the relation between OLS, MM (method of moments) and ML (maximum likelihood)? During my studies, the three concepts got taught completely separated from each other. However, they seem to be ...
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### Poisson Process Method of Moments

Disclaimer: This is a homework problem A School of Ornithology researcher wants to estimate the number of red-tailed hawks in Ithaca. She radio tags 10 birds, and then sets up a feeding station with ...
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### Method of Moments for Mixture distribution

The restaurant owner also wants to reconfigure her seating layout, and has asked you for help in modeling her clients. She gives you a dataset of past reservations, and tells you that she gets a mix ...
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### Is this estimator biased or unbiased?

A random variable X constructed as follows: $$X = \sum_{i=1}^{N} Z_i \$$ where $N$~Poisson$(\lambda)$ with $\lambda > 0,\space$ and$\space$ {${{Z_i}}$}$^N_{i=1}$ is an independent and identically ...
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### Asymptotic distribution of mme of coefficient of variation

For random sample from unif(0,1) distribution, method of moments estimator for coefficient of variation is sample mean divided by sample standard deviation. Here, coefficient of variation theta is mu/...
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### Weighted sum of negative binomial distributions - approximate fast parameter calculation

Let's suppose we have a convolution (weighted sum) of three negative binomials (parameterised as mean and overdispersion). ...
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### Method of moments as non-parametric model

In Wikipedia article (https://en.wikipedia.org/wiki/Nonparametric_statistics) about nonparametric statistics there is "Method of moments (statistics) with polynomial probability distributions&...
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### Can we use pooled ols on dynamic panel without individual fixed effect (but with group fixed effects) and no serial correlation in error

Is it correct that dynamic panel without individual fixed effect (but with group fixed effects), no serial correlation in error can be estimated consistently through pooled ols? For example, suppose ...
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### Confusion about method of moments for linear regression

It is known that linear regression estimator can also be viewed as a method of moment estimator derived using the moment condition $E[X\epsilon]=0$. This moment condition follows from exogeneity ...
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### Moments method and plug-in method

We have the following discrete distribution on $\{1,2,3\}$: $$\mathbb{P}(X=1)= \theta^2, \mathbb{P}(X=2) = 2\theta(1-\theta), \mathbb{P}(X=3)=(1-\theta)^2$$ with $\theta \in (0,1)$ and want to use ...
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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 ...
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### Method of moments when there's no closed form expression

I am trying to code up a method of moments algorithm for parameter estimation. I have a closed form for the moments as a function of the parameters, but these expressions are complicated, so there's ...
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### 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 ...
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### inverse of an exponential distribution

I have a question regarding this. Say I have $X_1, ..., X_n$ be random sample from an exponential distribution i.e. $Exp(\theta)$, and let $\gamma = \theta^2$. Let denote $\gamma^{mme}$ as the ...
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### “Appropriate conditions” for method of moments estimator to exist, be consistent, and asymptotically normal?

My statistics text has the following theorem, and alludes to "appropriate conditions on the model", but never specifies what those conditions are. What conditions are necessary? Let $\hat{\theta}_n$...
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### Deviations of Method of moments estimators for linear regression with constant

I am new to method of moments and want to figure out how to derive the method of moment estimator for $\beta$ in the linear equation with a constant term and three corresponding moments, namely, I ...
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### why is method of moments estimates asymptotically normal

I have noticed that a lot of statistics textbooks contain lengthy discussions and detailed proofs on showing that MLE estimates are asymptotically normal (under regularity conditions). On the other ...
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### Approximating standard error that contains a parameter, by replacing the parameter with its estimate

I am a bit confused about the following step I have seen in the stats literature which seems to me a bit circular. Say you are approximating the standard error of the MoM estimate of an exponential ...
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### Suggesting a method of moments estimator for the chance that some event happens

Let $X_i$~ $\text{Pois}(\lambda)$ be the number of breakdowns a certain ATM machine experiences in the $i^{th}$ week. $\implies$ Let $\{X_i\}_{i=1}^n$ be iid of the number of breakdowns the machine ...