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

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Degrees of freedom of J-Test distribution

This book states, on page page 256 ( the GMM section) that the J-test(for over-identifying restrictions) is of the following form $G_n'J_n^{-1}G_n \approx \chi^2(m-p) $, where $G_n=G_n(\theta)=1/n ...
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1answer
39 views

Two stage GMM estimator in Matlab

I am trying to create a simple GMM estimator for the mean of a normally distributed random variable using the first three odd central moments of a normal distribution (all of which should be zero ...
5
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1answer
86 views

Required: Method of moments fitting routine for the two-parameter generalized Pareto

I am currently using the evd package which fits a two-parameter GPD by maximum likelihood. Since in small samples the MOM is superior to the ML estimation I'd like ...
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18 views

How to theoretically fit and test for t-distribution [duplicate]

I'm trying to test some data for the best distribution fit, and am looking to try the t-dist (all theoretically, no R computations) I think the best way to do this is to assume the distribution is ...
3
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1answer
75 views

Types of moments used in the method of moments?

In Wikipedia, the method of moments uses only ordinary moments: One starts with deriving equations that related the population moments (i.e., the expected values of powers of the random variable ...
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1answer
31 views

How would I assign the optimal weight matrix to combine the following moment conditions in MM?

The following information is given: Based on a sample x(n), with n = 1,..., 100 from the exponential distribution, we want to estimate lambda but the original data was lost; we only know that 38 ...
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1answer
32 views

GMM weight matrix $W_n$ — what does the index $n$ signify? [closed]

The question is as in the title. The GMM estimator (in my Econometrics notes) is as follows: $\hat \delta_{GMM}(W_n) = (S'_{xz} W_nS'_{xz})^{-1}(S'_{xz}W_ns_{xy})$
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58 views

Explaining generalized method of moments to an non-statistician

How do I explain Generalized Methods of moments and how it is used to a non statistician? So far I am going with it is something we use to estimate conditions such as averages and variation based on ...
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831 views

Examples where method of moments can beat maximum likelihood in small samples?

Maximum likelihood estimators (MLE) are asymptotically efficient; we see the practical upshot in that they often do better than method of moments (MoM) estimates (when they differ), even at small ...
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2answers
233 views

Is MLE more efficient than Moment method?

I have got some small data sets (about 8 to 11 data points for each set), following Normal distribution. I would like to find out the 95% confidence interval of the 0.005 and 0.995 percentile of each ...
4
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1answer
129 views

Hard thresholding a covariance matrix

I am new to the concept of thresholding a variance-covariance matrix and am having trouble understanding the exact process. I am following Bickel and Levina (2008) in choosing a hard threshold. What ...
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2answers
118 views

Derivation of the Satterthwaite appproximation

Using the method of moments, one can try to approximate the sum of $\chi_{r}^{2}$ variables as $\sum a_{i}Y_{i}$ by equating the $n$-th movements of the sample with the $n$-th movement of the ...
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141 views

Generalized method of moments versus standard least squares estimation

I was thinking that in a very standard case such as a simple linear model with iid errors and no endogeneity, I would get the same results using the a simple least square estimate (such as provided by ...
3
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1answer
93 views

What is the correct process of finding the point estimators for the following situation?

Let $X_1,X_2,...,X_n$ be a random sample from a uniform distribution on $(\mu-\sqrt 3\sigma,\mu+\sqrt3\sigma)$. Here the unknown parameters are two, namely $\mu$ and $\sigma$, which are the ...
2
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0answers
72 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
236 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 ...
2
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1answer
177 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 = ...
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1answer
64 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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57 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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65 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 ...
2
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2answers
170 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 ...
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1answer
443 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
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1answer
107 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
103 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 ...
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1k 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} + ...
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127 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 ...
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267 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
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1answer
332 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
569 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 ...
0
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1answer
272 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
395 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
344 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
116 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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1answer
926 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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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 ...
7
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1answer
1k 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?