线性模型中M检验原假设分布的随机加权逼近(英文)

Approximating Null Distribution of the M-Test Statistics in Linear Models

在线性模型中M-方法可以用于线性假设检验,其中M检验、Wald检验和Rao的计分型检验是最常用的检验准则.但是在计算这些检验的临界值时都涉及到未知参数的估计.在本文中我们利用随机加权的方法来逼近这些检验的原假设分布.结果表明在原假设和局部对立假设之下随机加权统计量的渐近分布与原检验统计量在原假设之下的渐近分布相同. 因此我们不需要对冗余参数进行估计,利用随机加权的方法就可以得到这些检验的临界值,而且在局部对立假设之下可以实现对功效的计算.当取不同的误差分布和不同的随机权时,我们对本文的方法进行了蒙特卡洛模拟.结果表明用随机加权方法来逼近原假设分布是非常精确的.

Linear hypotheses in linear models can be tested by the M-method. The M-test, the Waldtype test （W-test） and the Rao＇s score-type test （R-test） are the three most commonly used testing methods. However, the critical values for these tests are usually related to the unknown error distribution. In this paper, we propose random weighting resampling methods for approximating the null distribution of these tests. It is shown that under both the null and the local alternatives these random weighting test statistics all have the same asymptotic null distributions as that for the original test statistic. The critical values of these tests can therefore be obtained by the Monte Carlo random weighting method. An important feature of the proposed methods is that the approximation are valid even the null hypothesis is not true and the power evaluation is possible under the local alternatives. We conduct extensive simulations under different error distribution specifications and different choices of random weighting variables to assess performance of proposed method. The results show that the random weighting M-testing method can provide pretty accurate approximation of the null distribution.