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Is method of moments estimator unbiased?
The method of moments is the oldest method of deriving point estimators. It almost always produces some asymptotically unbiased estimators, although they may not be the best estimators. This method of deriving estimators is called the method of moments.
What is a method of moments estimator?
In statistics, the method of moments is a method of estimation of population parameters. It starts by expressing the population moments (i.e., the expected values of powers of the random variable under consideration) as functions of the parameters of interest. The solutions are estimates of those parameters.
Does the method of moments estimator always exist?
As it is well known, moment estimators could not be unique, and, what is more, they could not always exist. This occurs when the parameters of the Birnbaum–Saunders distribution are estimated by using the standard moment method.
How to calculate binomial distribution using method of moments?
From my sample, I got X ¯ = 3.99 and s 2 = 2.5757, so p ^ = 1 − s 2 / X ¯ = 0.3545 and then n ^ = X ¯ / p ^ = 11.2562, which I round to n ~ = 11. Then p ~ = X ¯ / n ~ = 0.3627. In truth, the data were simulated using n = 12 and p = 1 / 3.
Which is the method of moments estimator of μ?
We just need to put a hat (^) on the parameters to make it clear that they are estimators. Doing so, we get that the method of moments estimator of μ is: μ ^ M M = X ¯. (which we know, from our previous work, is unbiased). The method of moments estimator of σ 2 is: σ ^ M M 2 = 1 n ∑ i = 1 n ( X i − X ¯) 2.
Which is the method of moments for σ 2?
And, substituting the sample mean in for μ in the second equation and solving for σ 2, we get that the method of moments estimator for the variance σ 2 is: Again, for this example, the method of moments estimators are the same as the maximum likelihood estimators.
Which is the estimator for a binomial distribution?
In many applications of the Binomial distribution, $n$ is not a parameter: it is given and $p$ is the only parameter to be estimated. For example, the count $k$ of successes in $n$ independent identically distributed Bernoulli trials has a Binomial($n$,$p$) distribution and one estimator of the sole parameter $p$ is $k/n$.