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中文摘要：
基于替代样本和核实数据的统计分析对实际问题的研究具有重要意义．研究了替代样本与核实数据下的总体密度函数的估计问题，得到了递归型核密度估计量的强相合性的条件．
英文摘要：
It is very important for real problems to statistically analyze the surrogate and validation da- ta. The estimation of probability density functions of population with the surrogate sample and validation data is studied The strong convergence of recursive kernel estimation of probability density function under some appropriate conditions is proved.
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