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Suppose we have observed matrix-valued data $\bf X_1, \dots, \bf X_n$, which are assumed to be i.i.d. realizations of $\cal{MN}(\bf M, \bf U, \bf V)$. … \end{aligned} $$ I understand the MLE framework, but I wonder why this method does not work: Notice from the same Wikipedia page that $$\begin{aligned} \bf E[(\bf X - \bf M) (\bf X - \bf M)^\top] = \bf …

evaluation) to the topic of estimation (traditional materials include method of moments estimator, MLE, unbiasedness, efficiency, quantification of uncertainty), and what's a good way of organizing this … It would be great if you could suggest a reasonable arrangement of the two strands of topics. …

When estimating the parameters for GEV distribution by the Maximum Likelihood Method, having the log-likelihood function, one may try to find the maximum using a quasi-Newton method like Broyden-Fletcher-Goldfarb-Shanno … the method of moments. …

One reasonable method is to look at the form of the moments of the distribution and see if you can form closed form estimators using the method-of-moments or the method-of-quantiles, either for the general … the parameter expressions: $$\mu = \mathbb{E}(X_i) - \sqrt{\frac{6 \gamma^2}{\pi}} \cdot \mathbb{S}(X_i) \quad \quad \quad \quad \quad \sigma = \sqrt{\frac{6}{\pi}} \cdot \mathbb{S}(X_i).$$ Using a method-of-moments …

Here, $c$ and $M$ are a vector and a matrix in terms of moments ($m_r'$), and $h$ is a vector of estimators, say $\theta_1,\cdots,\theta_n$. … I would like to know if this paper utilizes the method correctly. Is the approximation really true for moments ($m_r'$)? Do you have any clue what $\Sigma$ is? …

The effect of taking logs on skewness and kurtosis depends on the distribution. … As Taylor points out, Taylor series (/the delta method) can be used to approximate moments of transformed variables, and even their distribution (under some conditions). …

I've been reading about method of moments and kernel density estimation, in order to understand if I can use them to fit my data to a pdf (even if not from the theoretical ones), but first I would like … If my answer isn't in any of the alternatives above, what should I be reading right now to advance? I need to fit it to make some conclusions about fuel and maintenance of the cars. …

The statement Moments based on the second instrument will dominate the minimization problem under equal weighting, wasting the information in the first. … GMM compared to vintage method-of-moments is exactly this increase in efficiency, since everything else can be achieved with MoM alone. …

Also, what in particular makes it better than the alternative approach -- method of moments? Also, I noticed that for the Gaussian, a simple scaling of the MLE estimator makes it unbiased. … The standard practice seems to be the plain computation of the MLE estimates, except of course for the well known Gaussian case where the scaling factor is well known. …

If you have a moderately large sample from a population known to be gamma, but with unknown parameters, then the parameters can be estimated by the method of moments or by the method of maximum likelihood … the population mode (one of them here). …

The approach of the exercise is to find a MVUE for some non-standard descriptor $E[Y]$ of a distribution by applying a method of moments where we express the descriptor $E[Y]$ in terms of distribution … The method of moments is the wrong direction when it equates $E[(X_1 − \theta_1)^4]$ to the observed 4th moment $ \sum_{i=1}^n \left(X_i - \overline X\right)^4$. …

For part (a), it is well known as to how we can find central moments using the mgf technique (see for instance here). My question: Why did the authors ask part (a)? … Usually, they do that to nudge the reader towards the method to solve part (b). …

The risk of an estimator $t$ (which assigns a guess of $p$ to an observation $x$) is the expected loss of $t(X).$ It depends on the one thing you don't know: $p.$ Some risk functions will be better for … Identity guesses what was observed (it's the Maximum Likelihood and Method of Moments estimator), corresponding to $(t(0),t(1)) = (0,1).$ Inverted is an intentionally bad estimator that guesses $p=2/3 …

The Welch-Satterwaite approximation uses the method-of-moments The Welch-Satterwaite approximation is used to approximate a linear combination of scaled chi-squared random variables by a single scaled … The Welch-Satterwaite approximation uses the method of moments by equating the first two moments (mean and variance) under the true distribution and the approximating distribution. …

at $A=a_i$ and $f_{A|X}(a_i|x_i)$ is the conditional density of $A$ given $X$ evaluated at $a_i$ for a covariate profile of $x_i$. … It is possible to use other methods of density estimation, like kernel density estimation, or parameterizing a model to model both the conditional mean and other conditional moments. …