Weak Convergence and One-Sample Rank Statistics Under φ-mixing*
Canadian mathematical bulletin, Tome 18 (1975) no. 4, pp. 555-565

Voir la notice de l'article provenant de la source Cambridge University Press

Let {Xi:i=1, 2,...} be a real strictly stationary process (defined on a probability space (Ω, A, P)) which has absolutely continuous finite dimensional distributions (with respect to Lebesgue measure) and satisfies the φ-mixing condition: Let and denote the sub-cr-fields generated, respectively, by {Xi:i≤k} and {Xi:i≥k+n}; then, for each k≥1 and n≥l, and together imply.
Mehra, K. L. Weak Convergence and One-Sample Rank Statistics Under φ-mixing*. Canadian mathematical bulletin, Tome 18 (1975) no. 4, pp. 555-565. doi: 10.4153/CMB-1975-100-5
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[1] 1. Billingsley, Patrick, Weak convergence of probability measures, John Wiley & Sons, Inc., New York, 1968. Google Scholar

[2] 2. Chernoff, H. and Savage, I. R. Asymptotic normality and efficiency of certain nonparametric test statistics, Ann. Math. Statist., 29 (1958), 972–994. Google Scholar

[3] 3. Fears, T. R. and Mehra, K. L., Weak convergence of a two-sample empirical process and a Chernoff-Savage Theorem for ϕ-mixing sequences, Ann. Statist., 2 (1974), 586–596. Google Scholar

[4] 4. Pyke, R. and Shorack, G., Weak convergence of two-sample empirical process and a new approach to Chernoff-Savage theorems, Ann. Math. Statist., 39 (1968), 755–771. Google Scholar

[5] 5. Pyke, R. and Shorack, G. Weak convergence and a Chernoff-Savage theorem for random sample sizes, Ann. Math. Statist., 39 (1968), 1675–1685. Google Scholar

[6] 6. Pyke, R. and Shorack, G., A note on Chernoff-Savage theorems, Ann. Math. Statist., 40 (1969), 1116–1119. Google Scholar

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