Questions tagged [method-of-moments]

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

Filter by
Sorted by
Tagged with
25
votes
1answer
17k views

Link between moment-generating function and characteristic function

I am trying to understand the link between the moment-generating function and characteristic function. The moment-generating function is defined as: $$ M_X(t) = E(\exp(tX)) = 1 + \frac{t E(X)}{1} + \...
1
vote
0answers
188 views

How do I apply the method of moments for estimating parameters in a sum-relationship?

We have a model relationship between three random variables like this: $$ U = C + S $$ I have a ton of measurements of realizations of $U$, as well as a ton of realizations of $C$. But the ...
1
vote
0answers
976 views

Why doesn't the method of moments work when calculating the variance of the inverse gamma distribution?

I'm trying to calculate the variance of the inverse gamma distribution using the method of movements. According to wikipedia the variance should be: $$\sigma^2 =\frac{\beta^2}{(\alpha-1)^2(\alpha-2)}$...
2
votes
1answer
2k views

method of moments with variance=$\sigma^2$

I am trying to estimate the value of a parameter by equating variance from a distribution to the sample variance... i.e. using method of moments estimation. Would it better to use the variance formula ...
2
votes
0answers
2k views

Estimating the parameters of a beta distribution with zeroes and ones in the sample

I have a list of values in [0,1] that I want to fit to a Beta distribution in order to get the corresponding alpha parameter. I can't use a beta fitting function because my values might be 0's and 1'...
1
vote
1answer
2k views

Non-Bayesian alternatives to maximum likelihood estimators and method of moment estimators when there's only one observation

When trying to estimate the parameters of a known distribution, it might occur that the maximum likelihood estimator and the method of moment estimator don't work well when there's only one ...
2
votes
1answer
2k views

Deriving OLS estimates using method of moments

I've worked the slope all the way down to $\sum [x_i(y_i - \bar{y})] = \hat\beta_1 \sum[x_i(x_i - \bar{x})]$ But I can not figure out how to show the steps for: $\sum[x_i(y_i - \bar{y})] = \sum(x_i -...
4
votes
3answers
486 views

Fitting a pdf against Weibull pdf

I have a pdf function as follows: $$\dfrac{1}{s+a-b} [bs e^{-bt} + (a-b)(s+a)e^{-(s+a)t}]$$ I want to fit this against a weibull pdf with shape=1.12 and scale=461386. I want to calculate the values of ...
3
votes
1answer
282 views

Generalize the usage of moments in method of moments?

In Method of Moments for estimation, if there are $k$ parameters to estimate, we usually consider $i$-th moments, $i=1,...,k$, so that we have k equations for k unknowns. I wonder if it is wise to ...
3
votes
1answer
3k views

What's a good introduction to simulated method of moments and the extended path technique?

I'm reading a paper by Stephane Adjémian on DSGE modeling with a zero lower bound for the nominal interest rate, and he's using what he describes as the simulated method of moments / extended path. ...
11
votes
2answers
6k views

How do I know which method of parameter estimation to choose?

There are quite a few methods for parameter estimation out there. MLE, UMVUE, MoM, decision-theoretic, and others all seem like they have a fairly logical case for why they are useful for parameter ...
15
votes
1answer
5k views

What is the difference/relationship between method of moments and GMM?

Can someone explain to me the difference between method of moments and GMM (general method of moments), their relationship, and when should one or the other be used?

1 2 3
4