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受限自适应下单样本秩检验的渐近亏损AI 解读

In this paper we consider adaptive one-sample rank tests of the following type: the score function $J$ of the test is estimated from the sample under the restriction that $J \in \mathscr{J}$, for some given one-parameter family $\mathscr{J} = \{J_r, r \in I \subset R^1\}$. Using deficiencies, we compare the performance of such tests to that of rank tests with fixed scores. Conditions on the estimator $S$ of the parameter $r$ and on $J_r$ are given, under which the deficiency…

依赖情形下正态总体均值的检验AI 解读

Modifications of the $t$-test are considered which are robust under certain violations of the independence assumption. The additional number of observations these modified tests require in order to obtain under independence the same power as the $t$-test, is obtained asymptotically.

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Kendall秩相关系数的Edgeworth展开札记AI 解读

In this note it is shown how to some extent the Edgeworth expansion for the distribution function of Kendall's $\\tau$ can be established by using a well-known general result on such expansions.

自回归依赖下的单样本秩检验AI 解读

One-sample linear rank tests are considered for the case where the observations are not independent but come from an autoregressive process. It is proposed to apply the tests under these circumstances to certain transformations of the observations, rather than to the observations themselves. Then the tests have asymptotically the same properties as under independence, both under the hypothesis and under contiguous location alternatives. In particular, they are asymptotically…

单样本问题中分布无关检验功效的渐近展开AI 解读

Asymptotic expansions are established for the power of distribution free tests in the one-sample problem. These expansions are then used to obtain deficiencies in the sense of Hodges and Lehmann (1970) for distribution free tests with respect to their parametric competitors and for the estimators of location associated with these tests.