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Complete asymptotic expansions for the two-sample problem

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Abstract

Let x1, x2,...,xn and y1, y2,...,yn be the results of two series of independent observations. Let us denote by FR 1 (x) and GR 2 (y) the empirical distribution functions constructed on the basis of the first and the second sample, respectively. Let us write

This paper deals with a complete asymptotic expansion, for the case n1=n, n2=np, n→∞ of the probability

in a power series 1/√n, where p⩾1 is a fixed integer, and λ1>0 and λ2> 0 are fixed positive numbers.

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Authors
  1. Yu. V. Borovskikh
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 53, pp. 4–53, 1975.

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Borovskikh, Y.V. Complete asymptotic expansions for the two-sample problem. J Math Sci 12, 141–177 (1979). https://doi.org/10.1007/BF01262716

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