截断样本下的强率函数和密度函数核估计的渐进正态性

本文用[1]发展的计数过程去研究截断样本下强率函数核估计的渐进正态性．在弱于[7]和[10]的条件下，得到了更一般的结果．接着我们将这种方法运用到密度函数核估计，在较弱的条件下，得到了截断样本下密度函数核估计的渐进正态性．     

Asymptotic normality of the nearest neighbor hazard estimates

1.IntroductionSupposethatXI)')Xu,'beani.i.d.sequenceofrandomvariableswithdistributionfunctionF(x)anddensityfunctionf(x).TOestimatethedensityfunctionatxbasedonthefirstnobservations,thekerneltypeestimategiveswhereK')isakernelfunction,R.(x)isabandwidthsequenceandFi')isanestimateofF,usuallytakentobetheempiricaldistributionfunction.Formoredetails,see[21.Inmedicalapplications,itisoftenmoreimportanttoestimatethehazardfunctiondefinedbyA(x)~f(x)/(1--F(x)).IfXrepresentsalife-time,thenA(x)repre…