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Suppose we have a random sample \(X_1, X_2, \cdots, X_n\) whose assumed probability distribution depends on some unknown parameter \(\theta\). Our primary goal here will be to find a point estimator \(u(X_1, X_2, \cdots, X_n)\), such that \(u(x_1, x_2, \cdots, x_n)\) is a "good" point estimate of \(\theta\), where \(x_1, x_2, \cdots, x_n\) are the observed values of the random sample. More @Wikipedia
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- 1.2 - Maximum Likelihood Estimation | STAT 415 - Statistics OnlineMaximum likelihood estimates. Definition. Let X 1, X 2, ⋯, X n be a random sample from a distribution that depends on one or more unknown parameters θ 1, θ 2, ⋯, θ m with probability density (or mass) function f (x i; θ 1, θ 2, ⋯, θ m). Suppose that (θ 1, θ 2, ⋯, θ m) is restricted to a given parameter space Ω. Then:
- Maximum likelihood estimation - WikipediaIn statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed statistical model, the observed data is most probable.
- Topic 15: Maximum Likelihood Estimation - The Department of MathematicsThe maximum likelihood estimator (MLE), ^(x) = arg max L( jx): (2) We will learn that especially for large samples, the maximum likelihood estimators have many desirable properties. However, especially for high dimensional data, the likelihood can have many local maxima.
- Probability concepts explained: Maximum likelihood estimationA beginners introduction to the maximum likelihood method for parameter estimation (mle). It explains the method and goes through a simple example to demonstrate.
- 20: Maximum Likelihood Estimation - Stanford UniversityMLE of the Poisson parameter, N %&’, is the unbiased estimate of the mean, $J(sample mean)
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