algebraic.mle

Algebraic Maximum Likelihood Estimators

The maximum likelihood estimator (MLE) is a technology: under regularity conditions, any MLE is asymptotically normal with variance given by the inverse Fisher information. This package exploits that structure by defining an algebra over MLEs. Compose independent estimators into joint MLEs via block-diagonal covariance ('joint'), optimally combine repeated estimates via inverse-variance weighting ('combine'), propagate transformations via the delta method ('rmap'), and bridge to distribution algebra via conversion to normal or multivariate normal objects ('as_dist'). Supports asymptotic ('mle', 'mle_numerical') and bootstrap ('mle_boot') estimators with a unified interface for inference: confidence intervals, standard errors, AIC, Fisher information, and predictive intervals. For background on maximum likelihood estimation, see Casella and Berger (2002, ISBN:978-0534243128). For the delta method and variance estimation, see Lehmann and Casella (1998, ISBN:978-0387985022).

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