Abstract This paper proposes and studies a novel test for the geometric distribution which is based on a characterization of that law in terms of the conditional expectation of the second order statistic, given the value of the first order statistic. The asymptotic null distribution of the test statistic and its limit under general conditions are derived, proving that it is consistent against fixed alternatives. It can also detect alternatives converging to the null at the rate n − 1 ∕ 2 , n denoting the sample size. A weighted bootstrap and a parametric bootstrap can be used to consistently estimate the null distribution. The finite sample performance of these two bootstrap approximations is assessed via simulation. The power of the new test is numerically compared with that of some existing tests, concluding that the proposal presents a competitive behavior.

中文翻译：

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基于阶次统计线性回归的几何分布检验

摘要 本文提出并研究了一种几何分布的新检验，该检验基于该定律在二阶统计量的条件期望方面的特征，给定一阶统计量的值。推导出检验统计量的渐近零分布及其在一般条件下的极限，证明它与固定备选方案是一致的。它还可以检测以 n − 1 ∕ 2 的速率收敛到零的替代方案，n 表示样本大小。加权引导程序和参数引导程序可用于一致地估计零分布。这两个自举近似的有限样本性能是通过模拟来评估的。新测试的功效与一些现有测试的功效进行了数值比较，