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STRONG L1-NORM CONSISTENCY OF DATA BASED HISTOGRAM ESTIMATES OF DENSITIES
【摘要】 <正> In this paper we investigate the problem of estimating the d-dimensional probability densityf（x）,x∈Rd from a sample of size n.The non-parametric estimator is the data based histogram fn（x）as defined in （1）.Under suitable conditions,we have proved the L1-norm consistance of this estimate,that is（?）interal from Rα|f（x）-fn（x）|dx=0, a.s.
【Abstract】 In this paper we investigate the problem of estimating the d-dimensional probability densityf（x）,x∈Rd from a sample of size n.The non-parametric estimator is the data based histogram fn（x）as defined in （1）.Under suitable conditions,we have proved the L1-norm consistance of this estimate,that is（?）interal from Rα|f（x）-fn（x）|dx=0, a.s.
【关键词】 histogram；
estimator；
estimating；
parametric；
Probability；
uniformly；
lemma；
Borel；
measurable；
少子；
- 【文献出处】 Acta Mathematicae Applicatae Sinica(English Series) ,应用数学学报(英文版) , 编辑部邮箱 ,1985年04期
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