Meanings of asymptotic distribution in English

The asymptotic distribution properties of the test statistics are derived by means of martingale techniques.

The asymptotic distribution of the new test statistics is established and a simulation study is conducted.

We establish the asymptotic distribution for the proposed statistic and conduct theoretical analysis on its power.

We present an algorithm to estimate the scale function nonparametrically, and obtain asymptotic distribution theory for regression parameter estimates.

Our estimators have closed-form solutions, and their asymptotic distributions can be derived.

Postmodel selection inference was conducted via a bias-correction method, for which the asymptotic distributions were derived.

Furthermore for the test procedures whose asymptotic distributions have been derived, the results are only for the null hypothesis.

In this paper, a new class of generalized log-rank tests is proposed and their asymptotic distributions are derived under both null and alternative hypotheses.