The method-of-moments tag has no wiki summary.
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How to choose grid for SMM and report results?
In estimating a model with two variables by simulated method of moments. How does one generally choose the number of points on the grids? For example, consider one variable as interest rate between 0% ...
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23 views
Need to find a parameter space [closed]
I have the following problem:
Let $Y_1,Y_2,...,Y_n$ denote a random sample from the probability density function
$$f(y| \theta)= \begin{cases} ( \theta +1)y^{ \theta}, & 0 < y<1 \\ 0, ...
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0answers
41 views
Method of moment estimator
Consider $U_i \sim^{iid} Bernoulli(\pi)$. Also consider:
$$Y_i | U_i = 0 \sim exp(1/\gamma) \text{ and } Y_i | U_i = 1 \sim exp(1/2\gamma) $$
What are the method of moment estimators of $\pi \text{ ...
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1answer
90 views
t distribution method of moments
This is a further question to my original question, where I did not get an helpful answer (at leas not helpful for me) :Methods of moments for t distribution
I want to fit a t distribution to my data ...
0
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1answer
67 views
Methods of moments for t distribution
The parameters of a t distribution can be estimated via
1) ML or
2) method of moments
If we use the method of moments we have:
$\mu=E(R)$
$\sigma^2=V(R)=\frac{\beta \nu}{\nu -2}$
$\kappa = ...
1
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1answer
46 views
Finding moments for a theoretical density function
I am working on finding higher order moments for a given theoretical function, to be used in modelling of daily log-returns. The PDF is,
$f_r(x) =$
$\begin{cases}
\quad ...
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0answers
30 views
Is it possible to calculate mutual information by moments generating functions?
I went to listen to a workshop and some audience asked the presenter how the moments can improve the mutual information. I am learning the MI(Mutual Information) and moments so don't have enough ...
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39 views
Confusion about using moment condition in a multiple regression model
The very simple case assumes that we have a model like $y = a + bx + e$ where the condition $cov(x,e)=0$ is true. Hence one can use the relationship of the moment conditions to estimate the parameter ...
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1answer
67 views
Local maxima anomalies of likelihood methods
Likelihood methods have many desired properties. Sadly, local maxima in finite samples is not one of them. The fact a local maximum exists near the true parameter value is of no comfort if one ...
1
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1answer
268 views
Show that $\hat\theta=\frac{2 \bar Y- 1}{1- \bar Y}$ is an unbiased estimator for $\theta$
Let $Y_1,Y_2,...,Y_n$ denote a random sample from the probability density function
$$f(y| \theta)= \begin{cases} ( \theta +1)y^{ \theta}, & 0 < y<1 , \theta> -1 \\ 0, & ...
3
votes
1answer
76 views
Question about inverse in a two-step estimator as a joint GMM-estimators approach
I'm reading Newey & McFadden - Large sample estimation and hypothesis testing (in the Handbook of Econometrics, Volume 4, 1994, page 2178).
My model which I'm interested in has some former ...
2
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1answer
72 views
Deconvolution with fourier transform or characteristic function?
Let us consider the following model:
$$Y_j = X_j + \epsilon_j \hspace{15pt} j=1, ..., n$$
Where $Y_j$ is a noisy signal, $\epsilon_j$ is the noise which is independend from the signal $X_j$. We have ...
4
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1answer
368 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:
$$
M_X(t) = E(\exp(tX)) = 1 + \frac{t E(X)}{1} + ...
1
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0answers
97 views
How do I apply the method of moments for estimating parameters in a sum-relationship?
We have a model relationship between three random variables like this:
$$ U = C + S $$
I have a ton of measurements of realizations of $U$, as well as a ton of realizations of $C$. But the ...
1
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0answers
139 views
Why doesn't the method of moments work when calculating the variance of the inverse gamma distribution?
I'm trying to calculate the variance of the inverse gamma distribution using the method of movements. According to wikipedia the variance should be:
$$\sigma^2 ...
2
votes
1answer
222 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 ...
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0answers
303 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 ...
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0answers
148 views
Derivation of variance of a Poisson distribution from first factorial moment [closed]
Is there a way to derive the variance of a Poisson distribution using the first factorial moment only?
0
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1answer
141 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
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1answer
226 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 ...
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3answers
290 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
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1answer
84 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 ...
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vote
1answer
507 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. ...
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2answers
1k 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 ...
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1answer
685 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?
