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Summary:
The paper deals with the problem of testing independence of a pair of random variables $X=W+\Delta ,\ Y=W^*+\Delta Z$ by locally most powerful rank tests in a neighborhood of the point $\Delta =0$. The corresponding tests for double-exponentially and for normally distributed random variables $W$ and $W^*$ are introduced. The power-functions of the $U$-test in a neighborhood of the points $\Delta =\rho =0$ for both cases are given numerically.
References:
[1] Elandt, Regina: Exact and Approximate Power of the Non-parametric Test of Tendecy. Ann. Math. Stat. 33, 471-481, 1962. DOI 10.1214/aoms/1177704574 | MR 0137239
[2] J. Hájek Z. Šidák: Theory of Rank Tests. Academia Praha 1967. MR 0229351
[3] I. P. Natanson: Teorija funkcij veščestvennoj peremenoj. Moskva 1957.
[4] Tables of the Binomial Probability Distribution. Nat. Bur. of Stand. Appl. Math. Ser. 6, 1950.
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