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存在仅在备择下可识别的干扰参数时，曲指数族中的似然比检验AI 解读

For submodels of an exponential family, we consider likelihood ratio tests for hypotheses that render some parameters nonidentifiable. First, we establish the asymptotic equivalence between the likelihood ratio test and the score test. Secondly, the score-test representation is used to derive the asymptotic distribution of the likelihood ratio test. These results are derived for general submodels of an exponential family without assuming compactness of the parameter space.…

经验鞍点与自助法尾部近似的小相对误差概率界AI 解读

To obtain test probabilities based on empirical approximations to the distribution of a Studentized function of a mean, we need the approximations to be accurate with sufficiently high probability. In particular, when these test probabilities are small it is best to consider relative errors. Here we show that in the case of univariate standardized means and in the general case of tests based on smooth functions of means, the empirical approximations have asymptotically small…

最小对比估计量的密度AI 解读

Conditions for the existence of the density of a minimum contrast estimator in a parametric statistical family are given together with a formula for this density. The formula is exact if multiple local minima cannot occur; otherwise the formula is an exact expression for the point process of local minima of the contrast function. Although it is not in general feasible to compute the expression for the density, the formula can be used as a basis for further expansion of the…

方向性检验概率的鞍点展开AI 解读

SUMMARY An expansion is derived for the conditional tail probability of a multivariate random variable given its direction from the expected value. In particular, if the score function of a statistical model is chosen as this variable, such a conditional probability gives a test for a simple hypothesis, which is asymptotically equivalent to the likelihood ratio test. The expansion is of the large deviation type and is derived through the use of saddlepoint methods. Thus the…

渐近辅助性的二阶研究AI 解读

The paper deals with approximate ancillarity as discussed by Efron and Hinkley (1978). In the multivariate i.i.d. case we derive the second-order Edgeworth expansion of the MLE given a normalized version of the second derivative of the log-likelihood at its maximum. The expansion agrees with the one derived by Amari (1982a) for curved exponential families, but holds for any family satisfying the regularity conditions given in the paper. It is shown that the Fisher…