ψ-混合样本核密度估计的强一致相合性
THE STRONG UNIFORM CONSISTENCY OF KERNEL DENSITY ESTIMATES FOR φ—MIXING SAMPLE
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摘要: 本文研究了基于φ-混合样本且核为可变化的密度函数估计的强一致相合性,获得了与独立同分布样本时同样优良的收敛速度O(（n/logn）-1/3).Abstract: Let X1, X2, … be a φ-mixing Sample with density function f（x）, fn（x1, Kn）=\frac1n h_n \sum_i=1^n K_n\left(\fracx-X_ih_n\right), be an estimate of the f（x）, under proper conditions, we obtain he best convergence rate \sup _\epsilon \in J\left|f_n\left(\infty, K_n\right)-f(x)\right|=O\left((n / \log n)^-1 / 3\right), a.s..
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