正交级数密度估计积分平方误差的极限定理(英文)

Limit Theorem for Integrated Square Error of Orthogonal Series Density Estimators

论文研究了密度函数正交级数的积分平方误差 (ISE)的渐近性质 .在相当弱的条件下 ,证明了ISE正则化后的渐近分布等同于一列独立的中心化后的

The limiting distribution for is derived integrate d square error(ISE) of nonparametric density estimators based on orth ogonal series under some mild conditions, and it is proved that the limiting dis tributi on of the standardization of ISE is the distribution of a linear combination of independent centred χ 2 1 random variables.