Revision #597 → #1398 · back to history
addedMaximum likelihood estimatione2226c7675ff
addedLikelihood functionbe3fea203cf0
addedLikelihood factorizes for independent variables6cfda0ee4e3b
addedMLE as maximizer of likelihoodbf24d9f3d3ea
addedMaximum likelihood estimate8258a1a27fb2
addedMaximum likelihood estimator921ac12c12a1
addedSufficient condition for existence of MLE9a3f7195adde
addedLog-likelihood2119eb3c9fe1
addedLikelihood equationse5bf66cce0ad
addedNegative semi-definite Hessian indicates local maximum4ae498a19832
addedConstrained MLE optimization38280109bcae
addedRestricted likelihood equations via Lagranged479ddb5ca6b
addedLagrange multiplier test66940f0ead81
addedNonparametric MLE via empirical likelihooda4c98a39af68
addedMLE as extremum estimatora5103e50ca36
addedLimiting properties of MLE27f476471a35
addedConsistency of the MLE59bc66189b02
addedMLE converges in probabilityfb663176d18a
addedMLE converges almost surely963847d4ba8a
addedIdentification condition45808718085a
addedCompactness conditionf05510d8024d
addedContinuity condition9a6cd8c7ddc7
addedDominance condition2cf29dd57a9a
addedAsymptotic normality of the MLE411f0edbed1b
addedFunctional invariance of the MLE9328f61b6f1d
addedProfile likelihoodb0e453a560c2
addedEquivariance under data transformations293f262a114c
addedLog-normal MLE equals normal MLE of logs0caf3e653bad
addedAsymptotic efficiency reaches Cramér–Rao bound3b59a0600872
addedBias zero up to order 1/√n2731e2ea0caf
addedMLE has bias of order 1/n1440a3f271fd
addedBias-corrected maximum likelihood estimatoref627a2da7c7
addedSecond-order efficiency of bias-corrected estimator5452ccfb387c
addedMLE coincides with MAP under uniform prior660077f200a9
addedBayes Decision Rule809748a62b81
addedBayes rule under zero-one loss48a61fe7ef26
addedMLE minimizes Kullback–Leibler divergencef5196aec2dbf
addedMLE minimizes cross entropy5cb156e6d5c6
addedPrediction bias of MLE9f5590170496
addedDiscrete uniform distribution MLE07e40ac2f878
addedUnfair coin, finite parameter space5012e90bfc9b
addedBernoulli MLE, continuous parameter spaceeb241796762b
addedGeneralized Bernoulli MLE s/n4e79e802f859
addedMLE for the normal distributionf604ff140827
addedSample-mean MLE is unbiased263a741aebb4
addedVariance MLE is biased9c9266a17bb6
addedNormal log-likelihood at maximum8d54b119c3c1
addedIndependence via factorized density835e8fcfd7ec
addedMultivariate normal joint density88d68edea610
addedBivariate normal joint density9aebdebf3b24
addedMultinomial joint probability985508bc50c1
addedConstrained multinomial MLE via Lagrange38ecac32d3a7
addedLikelihood equations not solvable explicitly354db22f05ff
addedIterative updating formula89ff0c6230ab
addedGradient descent method17f8e308b6fe
addedNewton–Raphson step689ae91df16d
addedBerndt–Hall–Hall–Hausman algorithmfdf53aad4336
addedQuasi-Newton secant updatese689a65d7050
addedDavidon–Fletcher–Powell formulaaa8d46f60092
addedBFGS algorithm69408a54caea
addedBFGS convergence conditionc4a991be8bb1
addedFisher scoring algorithmec2e269d073f
addedQuasi-Newton convergence to stationary point6a79c5ec13fc
addedWilks' theoreme6d65116adab
addedAsymptotic chi-squared distribution of log-likelihood errorde6cd2d127b8