In this paper we consider robust parameter estimation based on a certain cross entropy and divergence. The robust estimate is defined as the minimizer of the empirically estimated cross entropy. It is shown that the robust estimate can be regarded as a kind of projection from the viewpoint of a...

It is well known that Bartlett adjustment yields an improvement on the chi-squared approximations to the likelihood ratio test statistics. However, it is not possible to obtain such an improvement for some test statistics. Typical examples are the score test statistic and...

We obtain useful estimators of the parameters, without recursion computations, under the random coefficient model with unbalanced data. These estimators reduce to the maximum likelihood estimators in a special case. The consistency is shown under some moderate assumptions.

The variance stabilizing transformation and the studentization have a simple relation on the skewness and the mean. The resultant relation implies that the former makes a better normal approximation than the latter for estimators of correlation coefficient in some cases, including an elliptical...

In the present paper, we consider the likelihood ratio criterion (LRC) for mean structure in the growth curve model with random effects. It is difficult to express the LRC as a closed form because of a restriction on parameters. The lower bound and upper bound of the LRC are suggested as a...

The conditional maximum likelihood estimator is suggested as an alternative to the maximum likelihood estimator and is favorable for an estimator of a dispersion parameter in the normal distribution, the inverse-Gaussian distribution, and so on. However, it is not clear whether the conditional...