# What are the general methods for parameter estimation in statistics?

I have a task to estimate the probability of evolution selection of a given node.

The only parameter estimation method I can think of is using the law of large numbers, i.e., use the proportion to estimate the probability. There are definitely many other parameter estimation methods, like the genetic algorithm, etc.

Is there a good reference to the general methods for parameter estimation?

• I recommend you take an introductory Statistics course. Jun 16, 2015 at 22:54

I'm not aware of a single-reference that I think gives particularly good coverage of the gamut of typical methods; a reference that's great on MLE may not be so great on Bayesian methods or might omit any discussion of quantile matching or minimizing a goodness of fit statistic, and some of the best reference on Bayesian methods tend to focus only on that. [It's also not really clear whether you're after the theory of estimation or mainly more practical information.]

As such, I'll list some approaches to help focus your search for the kinds of things you may want ... you might find books or other references which offer good coverage of one or more of these topics, with whatever emphasis on theory or practice you may want, but it may take several books to get good overall coverage.

Given a statistical model for your data-generating process, there are numerous common ways to estimate parameters in that model, of which I'll list a few:

i) maximum likelihood (MLE)

ii) moment matching ("method of moments")

iii) quantile matching

iv) optimizing some criterion of fit (e.g. - in different situations on might consider minimum chi-square, least squares, minimizing a goodness of fit statistic, or any number of other possibilities)

v) backing out an estimate (and perhaps a CI for the parameter) from a hypothesis test; this is not unusual with nonparametric tests, for example. There's an example of estimating the slope of a line via a Spearman correlation here; another common example would be estimating and obtaining an interval for a location shift between two groups using Wilcoxon-Mann-Whitney test.

vi) Bayesian methods (which in turn could be split into a number of topics like MAP, MMSE, and so on)

MLE and related methods are very popular, as are Bayesian methods; in some applications use of method of moments and related approaches are quite common.

There are many textbooks that cover basics of estimation theory, maximum likelihood estimation, and offer a little on method of moments and/or Bayesian methods, but it's not clear to me whether or not they'd lean more toward the 'theory' side than you'd really want.