L_1核密度估计的弱相合和完全相合性 |
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引用本文: | 胡舒合. L_1核密度估计的弱相合和完全相合性[J]. 安徽大学学报(自然科学版), 1993, 17(2): 11-17 |
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作者姓名: | 胡舒合 |
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摘 要: | 设x_n的密度函数为f(x),X∈R~d,f_n(x)=(nh~d)~(-1)sum from i-1 to n k((x-x_i)/h)为f的核估计,其中0
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关 键 词: | 核密度估计 弱相合性 完全相合性 |
The Weak and Complete Consistency in L_1 for Kernel Density Estimate. |
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Abstract: | Let f be a density on R~d and f_n be the kernel estimate of f, f_n (x) = (nh~d)~(-1) sum from i=1 to n K ((x-x_i)/h), where h=h_n→0 and K is an absolutely integrable function with ∫k(x)dx=1. Let J_n= f|f_n(x)-f(x)|dxwe give some sufficient conditions for J_n→0 in probability or J_n→0 complete- ly, where {x_n) is α-mixing or φ-mixing sample, which generalize the result in. |
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Keywords: | kernel density estimate weak consistency complete consistency |
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