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

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90 views

What is parameter identification in the context of OLS?

Can someone explain what identification means in the context of an OLS model? I have a fair grasp of the derivation using either the method of moments or by minimizing the squares, but am failing to ...
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0answers
8 views

Fully identified moment matching with simulated method of moments

I am struggling with some results regarding the model fit in this paper (p. 49). The authors set up a simulated method of moment estimator, using 8 different moments to match and 8 different ...
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2answers
261 views

Second Moment of Beta distribution

I am practicing the Method of Moments and in this problem, I am a little bit stuck on the algebra in my calculation of the second moment. I would sincerely appreciate any advice on what went wrong: ...
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1answer
30 views

Variance of estimator(exponential distribution)

I have exponential distributed data $Exp(\lambda)$ with sample n = 50. Also, The sample mean = 2.17. I need to find the estimator of parameter $\lambda$ by the method of moments and to build 95% ...
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1answer
57 views

GMM Estimator of an Exponential Distribution

Suppose you have to calculate the GMM Estimator for $\lambda$ of a random variable with an exponential distribution. $$f(x) = \lambda \cdot \exp(-\lambda\cdot x)$$ with $E(X) = 1/\lambda$ and $E(X^2) ...
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14 views

How to find the coefficient of parameters of shape and scale parameters of weibull distribution in Novel Energy pattern factor method?

Novel energy pattern factor method for Weibull distribution Please have a look on the paper for the further clarification of the question . Please help me out for finding out the coefficient of ...
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1answer
35 views

How to find method of moments estimator when 1 parameter is known and 1 is unknown? [closed]

Let X1,…,Xn be a random sample from a distribution with cumulative distribution function $$ F(x)= \begin {cases} 0 & \text{x < 0;}\\(x/β)^α & \text{0 ≤ x ≤ β;}\\ 1 & \text{x > β} \...
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2answers
107 views

Is it better to use a MLE or a MME to build an asymptotic confidence interval for a real parameter $\theta$?

I thought that the answer was pretty straightforward given that the MLEs possess some strong asymptotic properties, i.e. normality, efficiency and consistency. But then, I have found that also MME (...
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1answer
198 views

Is ANOVA relying on the method of moments and not on the maximum likelihood?

I see mentioned in various places that ANOVA does its estimation using the method of moments. I am confused by that assertion because, even though I am not familiar with the method of moments, my ...
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1answer
61 views

Proof that square of a standard normal r.v. has Chi-Square Distribution using MGF's

Supposes $Z \sim N(0,1)$. We know that $Z^{\top}\!Z\sim\text{Chi-Square}(1)$. Does the proof for this concept require the use of moment generating functions/method of moments per say?
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1answer
136 views

Bias of method of moments estimator for Pareto distribution with known scale parameter

Let $x$ be a Pareto distribution with a known scale parameter $m>0$, i.e. $x\sim f(x|a)=\frac{am^a}{x^{a+1}}, x>a, a>0$ $\mathrm{E}\left[X\right]=\frac{am}{a-1}$ Using method of moments ...
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1answer
48 views

What would be the method of moments (MOM) estimator of $\nu$ for t-distribution?

I recognize that method of moments is not the best way to estimate $\nu$ for the t-distribution, but I am just wondering how this would be calculated since $E[X^n] = 0$ if $n$ is odd. Here we're ...
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0answers
30 views

Covariance of parameter estimates in Method of Moments

I have a $3\times1$ vector function $f(x_i;\theta)$ where $X$ is a rv and $\theta$ is $3 \times 1$ parameter vector, such that \begin{equation} E \, f(X;\theta) = {\bf 0}.\end{equation} If I have a ...
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1answer
33 views

Does the second moment estimator of the uniform distribution parameter have the same properties as that of the first moment?

For independent and identically distributed samples $[y_1,...,y_m]$ where $y$ is uniformly distributed between $[0,\theta]$ with $0 \lt \theta \lt \infty$, finding the method of moments estimator for $...
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5answers
1k views

Maximum Likelihood Estimation — why it is used despite being biased in many cases

Maximum likelihood estimation often results into biased estimators (e.g., its estimate for the sample variance is biased for the Gaussian distribution). What then makes it so popular? Why exactly is ...
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0answers
105 views

approximate a probability distribution by moment matching

I have a 60-40 weighted distribution, of uniform(0,7.5) and uniform(7.5,10) respectively, i.e. $$f_X(x)=(0.6/7.5)1_{x∈[0,7.5)}+(0.4/2.5)1_{x∈[7.5,1]}$$ I have worked out that $$E(X) = 0.6(7.5/2) + ...
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0answers
27 views

method of moments for a non-standard distribution

Given data $X_1, ..., X_n$ iid distributed with probability density $C \exp(-(x-t)^4/4)$ for $-\infty < x < \infty$ where $C$ is the normalizing constant. Find the method of moment estimate of t....
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31 views

Fitting a nested model in SAS: maximum likelihood vs method of moments

I'm analyzing a nested design model in SAS (using proc mixed), but I'm not sure if I should be using restricted maximum ...
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2answers
53 views

Can I use other k moments for method of moments?

If I have 2 parameters, can I use, say 7th or 8th moments, instead of the first two moments to solve the equations? If yes, is there any difference?
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1answer
65 views

Method of moments for skew-t distribution

I'm trying to work out how to apply the method of moments to estimate the parameters of the skew-t distribution. From slide 12 of the following presentation: http://www.eief.it/files/2008/11/monti-8-...
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35 views

What is the computational complexity for Method of Moments?

If I want to measure the goodness of fit of an empirical distribution with N data points of dimension D to, e.g. a spherical Gaussian, using MoM, what is the order of complexity?
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1answer
173 views

MLE Fundamentals Question

So I'm a little stuck with what I feel is a basic question. The calculation is easy, but I've obviously missed a key concept of MLE. The Question Consider the family of models for the data X1,...,Xn ...
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1answer
282 views

Gaussian Mixture and Method of Moments

Given solely the first $n$ moments $m_1,\dots,m_n$ of a random variables $X\in\mathbb{R}$, I was wondering whether there exists a direct methodology to approximate $X$ with a Gaussian Mixture ?
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190 views

Estimating parameters in a truncated binomial distr

I would like to find the estimates of the parameters in a truncated (at zero) negative binomial distribution.Suppose $Z$ has this distribution with parameters ($\alpha,\beta$). (The parametrization ...
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4answers
396 views

What exactly are moments? How are they derived?

We are typically introduced to method of moments estimators by "equating population moments to their sample counterpart" until we have estimated all of the population's parameters; so that, in the ...
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0answers
47 views

Does diagnolizing higher-order cross-moment matrices lead to independent variables?

Diagonalizing the covariance matrix transforms multivariate data into uncorrelated variables, but does not make them independent necessarily. Does it follow from this that if I were to diagonalize ...
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2answers
884 views

What is the logic behind method of moments?

Why in "Method of Moments", we equate sample moments to population moments for finding point estimator? Where is the logic behind this?
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1answer
104 views

Is there any method to quantify parameter estimation uncertainty of method of moments fitting technique?

If I want to fit a distribution (let's say we can be certain about the type) to observations using maximum-likelihood method, I have many options to express the parameter estimation uncertainty due to ...
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2answers
245 views

What's the difference between estimating equations and method of moments estimators?

From my understanding, both are estimators that are based on first providing an unbiased statistic $T(X)$ and obtaining the root to the equation: $$c(X) \left( T(X) - E(T(X)) \right) = 0$$ Secondly ...
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119 views

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
3k 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 ...
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1answer
366 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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0answers
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
249 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
42 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
40 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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1answer
146 views

Explaining generalized method of moments to a 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 ...
46
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7answers
4k 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
579 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
385 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
247 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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1answer
694 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
144 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
108 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
466 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 ...
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1answer
743 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 = \frac{...
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1answer
87 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 \frac{1}{2}ae^{a\left(x-\mu\...
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0answers
100 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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96 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 $...
4
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3answers
239 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 ...