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基于离散最大惩罚似然准则的非参数密度估计AI 解读

A nonparametric probability density estimator is proposed that is optimal with respect to a discretized form of a continuous penalized-likelihood criterion functional. Approximation results relating the discrete estimator to the estimate obtained by solving the corresponding infinite-dimensional problem are presented. The discrete estimator is shown to be consistent. The numerical implementation of this discrete estimator is outlined and examples displayed. A simulation…

惩罚函数法下概率密度的非参数最大似然估计AI 解读

Tne maximum likelihood estimate of a probability density function based on a random sample does not exist in the nonparametric case. For this reason and others based on heuristic Bayesian considerations Good and Gaskins suggested adding a penalty term to the likelihood. They proposed two penalty terms; however they did not establish existence or uniqueness of their maximum penalized likelihood estimates. Good and Gaskins also suggested an alternate approach for calculating…