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Weak Convergence of a Two-Sample Empirical Process and a Chernoff-Savage Theorem for $|phi$ -Mixing SequencesWeak Convergence of a Two-Sample Empirical Process and a Chernoff-Savage Theorem for $|phi$-Mixing Sequences

Thomas R. Fears · K. L. Mehra刊期 1974-05-01 · 卷 2（3）The Annals of Statistics已编入正刊

φ混合序列的双样本经验过程弱收敛与Chernoff–Savage定理AI 解读

Using Pyke-Shorack (Ann. Math. Statist. (1968) 755-771) approach, based on weak-convergence properties of empirical processes, a Chernoff-Savage theorem concerning the asymptotic normality of two-sample linear rank statistics is proved for stationary $\phi$ -mixing sequences $\{X_m\}$ and $\{Y_n\}$ of rv's. This main result (Theorem 4.1) is almost as strong as proved by Pyke and Shorack for sequences of independent rv's. The basic tool employed is the following new result…Using Pyke-Shorack (Ann. Math. Statist. (1968) 755-771) approach, based on weak-convergence properties of empirical processes, a Chernoff-Savage theorem concerning the asymptotic normality of two-sample linear rank statistics is proved for stationary $\phi$-mixing sequences $\{X_m\}$ and $\{Y_n\}$ of rv's. This main result (Theorem 4.1) is almost as strong as proved by Pyke and Shorack for sequences of independent rv's. The basic tool employed is the following new result…

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被引 15 次 ↗OpenAlex · 核验 2026-10-04

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Weak Convergence of a Two-Sample Empirical Process and a Chernoff-Savage Theorem for ∣phi|phi∣phi-Mixing SequencesWeak Convergence of a Two-Sample Empirical Process and a Chernoff-Savage Theorem for $|phi$-Mixing Sequences

Weak Convergence of a Two-Sample Empirical Process and a Chernoff-Savage Theorem for $|phi$ -Mixing SequencesWeak Convergence of a Two-Sample Empirical Process and a Chernoff-Savage Theorem for $|phi$-Mixing Sequences