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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For Gamma distribution, use MLE or MoM?
For Gamma distribution, is it better to use MLE(maximum likelihood estimation) than MoM(method of moments) to estimate the shape and scale parameters?
Also, in python SciPy, does gamma.fit use MLE? I'...
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Method of moments for the Logarithmic/Log-Series distribution
I'm looking for some more insights in applying the method of moments for the Logaritmic (or also called Log-Series) distribution.
The Logarithmic distribution only has one distribution parameter $0 &...
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Why do popular ML and statistical packages simply ignore classical estimation and detection algorithms for statistical signal processing? [closed]
For those who had a hard time to study and understand classical estimation and detection algorithms, and unfortunately realized that these algorithms are simply ignored by many packages that have the ...
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How to calculate Gumbel with LMoments and GEV with method of moments
I need to calculate the values for certain return periods of a flood event (up to 5000). It has to be GEV with method of moments and Gumbel with L-Moments. But I am not sure about how to calculate ...
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How to build the covariance matrix with different weighted moments via GMM [closed]
I have two sets of moment conditions, one is IV moment with N observations but the second moment only has N_1 observations, N_1<N.
How to build the covariance matrix? Appreciate for any replies!
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Confidence interval for continuous uniform distribution [duplicate]
If X is a random variable from the uniform distribution on the interval [0,θ], how would one construct a 95% confidence interval for the method of moments estimator of θ?
I have found that
and also ...
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Motivation for using moment about mean versus moment about the origin
When calculating moments of probability distributions, what would motivate you to take the moment about the mean (called "central moment") versus the standard moment about the origin?
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Find nth central moment for exponential distribution
I am trying to figure out what the nth central moment is for the exponential distribution.
Here is the formula for the nth moment:
$$
\mathop{\mathbb{E}}{[x^n]} =\dfrac{n!}{\lambda^n}
$$
My question: ...
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Maximum likelihood vs generalized method of moments
I am trying to understand how maximum likelihood (MLE) and generalized method of moments (GMM) are related to each other. In particular, I often see people saying that MLE can be written in terms of ...
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How to take 1000 samples from distribution X and then use MLE to prove they came from distribution X?
I am trying to do:
find 1000 points that represent samples from distribution X with parameters $(a,b,c,\ldots, d)$
be guaranteed that the MLEs for those 1000 points are $(a,b,c,\ldots, d)$ with $99\%$...
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Is there any intuitive explanation for MoM in estimating parameters?
I found from some literature that when we use the method of moments to fit the Gumbel distribution, the estimated
(On page 24) A comparison of the variance formulas in (1.66) with the CramBr-Rao ...
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Confidence Interval for a MOM Estimator of a uniform distribution
If $X$ is a random variable from the uniform distribution on the interval $(\theta, 2\theta)$, how would one construct a 90% confidence interval for the method of moments estimator of $\theta$?
The ...
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Are these moments estimators asymptotic unbiased?
In this paper, authors consider method of moments of fitting Gumbel distribution:
We know that maximal likelihood estimators are asymptotic unbiased. But are these moments estimators asymptotic ...
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fit gamma distribution based on median interquartile range
I would like to create a gamma probability distribution in R with a median of 3 and interquartile range of [2,5]. I am familiar with the methods of moments to estimate the scale and shape of a gamma ...
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Calculate estimator of Θ using MOE and check if it is biased using its expected value
Observations $Y_1, Y_2, \ldots , Y_n$ are assumed to be independent and identically distributed samples from a
data model following a Rayleigh distribution, with probability density function:
$$ f(y;\...
Elena
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How do entropy-based estimators relate to more conventional ML, least square, and GMM estimators
Over the years i have done a lot of analysis, mostly of parameters of linear approximations to the data or a forecast, and I have used linear and nonlinear least squares, maximum likelihood, and GMM ...
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Is there a formula for estimating confidence intervals for indirect inference estimates?
Indirect inference is usually deployed to estimate parameters $\theta$ of simulation models, i.e. models for which likelihood is unknown or intractable but that can be "run forward" ...
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Using the Yule-Walker equation to calibrate an autoregressive model with the method of moments
Consider the following discrete autoregressive $\epsilon_t$, where $\epsilon_t \in (\pm 1 ) \forall \ t \geq 1$. We think of $\epsilon_t$ as the child of a previous sign at time $t-l$, where $l$ is ...
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Using the method of moments or GMM to estimate the parameters of a specific problem
Given $(X_t)_{t \in \mathbb{Z}}$ an AR(1) process:
$$X_t = c+ \phi X_{t-1} + \epsilon_t, \quad \epsilon_t\sim WN(0,\sigma^2)$$
We can show that $E(X_t) = \frac{c}{1- \phi}$ and $E(X_t^2) = \frac{\...
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Method of Moments for a mixing proportion
Suppose we have densities $f_1, f_2$ from the random variables $W_1$ and $W_2$ where $W_i$ has known mean $\mu_i$ and variance $\sigma_i$. Consider the mixture of the two densities $$ f(x;\theta)=\...
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In a regression model, can we use $E(u)=0$ as the moment condition?
Consider the linear model with stochastic regressors:
$$y_t = \beta_0^\prime x_t + u_t, \quad E(u_t | x_t)= 0$$
So that $E(u_t | x_t)= \beta_0^\prime x_t $. Using the e Law of Iterated Expectations (...
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Two supposedly equivalent approaches to the method of moments
I am reading the book "An Introduction to Econometric Theory" by A. Ronald Gallant. In the section of the book on the Method of Moments, I get a little confused about the method as I know it....
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A description of the mean of the Geometric Distribution - is it unorthodox or just incorrect?
I have a homework assignment where I'm asked to propose an estimator for the mean of a geometric random variable. This seemed simple enough, given that I've always understood the mean of the geometric ...
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Deriving unbiasedness of estimators (involving method of moments idea) of normal distribution with heterogeneous variance
I am currently reading this paper and in pp.127, 128, there are unbiased estimators that I cannot derive its unbiasedness.
The setting is simple. Let $$X_i\sim N(\mu,\tau^2+\sigma_i^2),\quad i\in\{1,\...
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Estimating $1/a$ for following pdf using method of moments estimation
A random sample of size $n$ is being drawn from a population with pdf as:
$$f(x) = \begin{cases} (a + 1)x^a & \text{for }0<x<1, \\
0 & \text{otherwise.} \end{cases}$$
Can we express the ...
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Using the methods of moments in R for the dirichlet distribution
I'm trying to build a distribution of transition probabilities to randomly sample from in a Markov model where individuals can transition from one health state to another (assume that in the image ...
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Method of moments estimate of Pareto Distribution
The Pareto distribution has the following $cumulative \ distribution \ function$ :
$$F(x;\alpha ,\Theta ) = \left\{\begin{matrix}
1 - (\frac{\alpha}{x})^{\theta}\ \ if \ \alpha \leq x\ & \\ 0 \ ...
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Finding method of moments estimate for density function $f(x|\alpha) = \frac {\Gamma(2\alpha)} {\Gamma(\alpha)^2}[x(1-x)]^{\alpha - 1}$
Suppose that $X_1, X_2, ..., X_n$ are i.i.d random variables on the interval $[0,1]$ with the density function
$$
f(x|\alpha) = \frac {\Gamma(2\alpha)} {\Gamma(\alpha)^2}[x(1-x)]^{\alpha - 1}
$$
where ...
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Efficiency of IV vs GMM
I am trying to understand how IV/just identified GMM and overidentified GMM compare when it comes to efficiency.
The way I understand it, we are able to identify the vector of coefficients in IV and ...
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Method of moments for symmetric mean zero distributions
When using the method of moments to fit a symmetric mean zero distribution, does it make more sense to fit higher order moments or lower order absolute moments? I could not find any resources which ...
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What's special about moments that allows "method of moments" to work?
The idea behind Method of Moments (MOM) is quite intuitive:
find the parameter values so that the population moments (which are functions of those parameters of interest) matches the sample moments.
...
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Consistent but inefficient GMM
Consider the following linear model
$$y_t = x_t' \beta +u_t$$
where $t =1,...,T$ and $x_t = (x_{1t} x_{2t} ... x_{kt})'$ , $ \beta$ is $k \times 1$ vector of unknown coefficients, $u_t$ is an iid ...
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Discuss that method of moment estimation is inefficient
Discuss that method of moment estimation is inefficient.
Then model is
Consider the following linear model
$$y_t = x_t' \beta +u_t$$
where $t =1,...,T$ and $x_t = (x_{1t} x_{2t} ... x_{kt})'$ , $ \...
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When is the Optimal weighting matrix in GMM singular?
currently I am trying to estimate a simple linear regression:
\begin{equation}
y_t = X \beta + \varepsilon_t,
\end{equation}
where I try to find 4 coefficients and one specific predictor is an ...
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1
answer
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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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Method of Moment for Gamma Distribution
I know that the empirical $r$-th moment is defined as:
$$\hat E(X^r) = \frac{1}{n} \sum_{i=1}^n x_i^r $$
So for the first moment I did:
$$E_{\lambda,\alpha}(X) = \hat E(X) = \bar X $$
$$\bar X = \...
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Confidence Interval for Estimator using Delta method
The statement
I am given the following discrete distribution with $\theta>0$
$$p(x) = \left(\frac{\theta}{1+\theta}\right) ^{2-x}\left(\frac{1}{1+\theta}\right)^{x-1} \hspace{1cm} x=1,2$$
I need to ...
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Method of moments and MLE
Suppose a random variable follows the logistic distribution, $X ∼ Logistic (\mu, \sigma)$ and we
restrict our attention to random samples drawn from this random variable $X$.
What would be the MoM and ...
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Method of Moment, MLE and Information matrix
We have $$\mathbb{E}[Y_i| X_i] = β_0 + β_1X_i$$
What would be the Method of Moments estimator and MLE for this model?
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Why methods of moments is not widely used in machine learning?
If I recall correctly, in most machine learning context I have encountered, only maximum likelihood estimation and maximum a posteriori method are used. Why not method of moments?
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MLE and Methods of Moments of Negative Binomial in R
Question
Let's say we define the Negative Binomial as follows:
$$f(x) = {x+r-1 \choose x} p^x (1-p)^r$$
With mean and variance:
$$E(x) = \frac{rp}{1-p} \quad \quad V(x) = \frac{rp}{(1-p)^2}$$
We are ...
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Variance of the method of moments estimator for $\mu$ of log-normal distribution
Suppose the data has originated from a log-normal distribution with parameters $\mu$ and $\sigma$ (i.e. the mean and standard deviation of the underlying normal distribution). I have only the sample ...
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Relation between OLS, MM and ML
What is the relation between OLS, MM (method of moments) and ML (maximum likelihood)? During my studies, the three concepts got taught completely separated from each other. However, they seem to be ...
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Poisson Process Method of Moments
Disclaimer: This is a homework problem
A School of Ornithology researcher wants to estimate the number of red-tailed hawks in Ithaca. She radio tags 10 birds, and then sets up a feeding station with ...
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Method of Moments for Mixture distribution
The restaurant owner also wants to reconfigure her seating layout, and has asked you for help in modeling her clients.
She gives you a dataset of past reservations, and tells you that she gets a mix ...
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Is this estimator biased or unbiased?
A random variable X constructed as follows:
$$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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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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