Maximum Likelihood Method

作者: Michael Zabarankin , Stan Uryasev

DOI: 10.1007/978-1-4614-8471-4_4

关键词: CombinatoricsScore testMultivariate random variableLikelihood functionScoreEstimation theoryProbability distributionMathematicsFinite setM-estimator

摘要: A classical problem in the statistical decision theory is to estimate probability distribution of a random vector X given its independent observations \(x_{1},\ldots,x_{n}\). Often it assumed that comes from some family functions parametrized by set parameters \(\theta _{1},\ldots,\theta _{m}\), so this case, reduced estimating _{m}\) and called parametric estimation. However, if no specific distributions assumed, i.e., can not be completely defined finite number parameters, nonparametric

参考文章(60)
Michael Zabarankin, Andrew Kurdila, Convex functional analysis ,(2005)
W. N. Venables, B. D. Ripley, Modern Applied Statistics with S Springer. ,(2010) , 10.1007/978-0-387-21706-2
Roger J‐B Wets, Statistical estimation from an optimization viewpoint Annals of Operations Research. ,vol. 85, pp. 79- 101 ,(1999) , 10.1023/A:1018934214007
James Franklin, The elements of statistical learning : data mining, inference,and prediction The Mathematical Intelligencer. ,vol. 27, pp. 83- 85 ,(2005) , 10.1007/BF02985802
R. Tyrrell Rockafellar, Stanislav Uryasev, OPTIMIZATION OF CONDITIONAL VALUE-AT-RISK Journal of Risk. ,vol. 2, pp. 21- 41 ,(2000) , 10.21314/JOR.2000.038
Jose Costa, Alfred Hero, Christophe Vignat, On Solutions to Multivariate Maximum α-Entropy Problems energy minimization methods in computer vision and pattern recognition. ,vol. 2683, pp. 211- 226 ,(2003) , 10.1007/978-3-540-45063-4_14
Włodzimierz Ogryczak, Andrzej Ruszczyński, On consistency of stochastic dominance and mean–semideviation models Mathematical Programming. ,vol. 89, pp. 217- 232 ,(2001) , 10.1007/PL00011396
A. D. Roy, Safety first and the holding of assetts Econometrica. ,vol. 20, pp. 431- ,(1952) , 10.2307/1907413
PETER J. ROUSSEEUW, KATRIEN VAN DRIESSEN, Computing LTS Regression for Large Data Sets Data Mining and Knowledge Discovery. ,vol. 12, pp. 29- 45 ,(2006) , 10.1007/S10618-005-0024-4