Convergence of the empirical two-sample -statistics with -mixing data
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In order to get rid of terms of the form bntkc and reduce the dependence in n, we will define for i ∈ In,u the random variable d X
by bounding |hq,s` (Xi)| by 2 and the terms i/n by 1. For the third condition, we also use ak = α (k), since each random variable Yni is a function of Xi. It remains to compute the limit of the sequence n−1 Var (Sn) n>1. By similar argument as those who gave (2.13), this reduces to compute for all 1 6 u 6 d + 1 the limit 2
i In,u
The second and third term cannot be treated similarly because of the terms i/n. Neverthe-less, we can use the following lemma. Download 380.03 Kb. Do'stlaringiz bilan baham: |
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