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Extremum estimator information


In statistics and econometrics, extremum estimators are a wide class of estimators for parametric models that are calculated through maximization (or minimization) of a certain objective function, which depends on the data. The general theory of extremum estimators was developed by Amemiya (1985).

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Extremum estimator

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In statistics and econometrics, extremum estimators are a wide class of estimators for parametric models that are calculated through maximization (or minimization)...

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Maximum likelihood estimation

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infinity). In frequentist inference, MLE is a special case of an extremum estimator, with the objective function being the likelihood. We model a set...

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Consistent estimator

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In statistics, a consistent estimator or asymptotically consistent estimator is an estimator—a rule for computing estimates of a parameter θ0—having the...

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Parameter space

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continuity of the objective function, suffices for the existence of an extremum estimator. In Deep Learning, the parameters of a deep network are called weights...

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List of statistics articles

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External validity Extrapolation domain analysis Extreme value theory Extremum estimator F-distribution F-divergence F-statistics – population genetics F-test...

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Law of large numbers

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result is useful to derive consistency of a large class of estimators (see Extremum estimator). Borel's law of large numbers, named after Émile Borel, states...

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Stochastic equicontinuity

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weak convergence, which can be used to prove the convergence of extremum estimators. Let { H n ( θ ) : n ≥ 1 } {\displaystyle \{H_{n}(\theta ):n\geq...

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Bayesian optimization

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ISBN 978-1107163447. Močkus, Jonas (1975). "On bayesian methods for seeking the extremum". Optimization Techniques IFIP Technical Conference Novosibirsk, July 1–7...

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Unimodality

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extension is a function with a single local extremum. One important property of unimodal functions is that the extremum can be found using search algorithms...

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Central limit theorem

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probability distribution Fisher–Tippett–Gnedenko theorem – limit theorem for extremum values (such as max{Xn}) Irwin–Hall distribution Markov chain central limit...

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Least mean squares filter

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of filter weights is a quadratic function which means it has only one extremum, that minimizes the mean-square error, which is the optimal weight. The...

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Data analysis

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ISBN 978-1-4725-6167-1, retrieved 2021-05-31 Nwabueze, JC (2008-05-21). "Performances of estimators of linear model with auto-correlated error terms when the independent...

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Density functional theory

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written as E[G]. However, G is determined not as its minimum, but as its extremum. Thus we may have some theoretical and practical difficulties. There is...

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