Shin-ichi Tsukada

Equivalence testing of mean vector and covariance matrix for multi-populations under a two-step monotone incomplete sample

This paper investigates the hypothesis testing of a mean vector and covariance matrix for multi-populations in the context of two-step monotone incomplete data drawn from N p + q ( µ , Σ ) , a multivariate normal population with mean µ and covariance matrix Σ . Three null hypotheses are considered, and the likelihood ratio criterion and Wald-type criterion are derived. On the basis of numerical simulations, the test that employs the Wald-type criterion is recommended.

Unbiased Estimator for a Covariance Matrix Under Two-Step Monotone Incomplete Sample

In this article, we consider an inference for a covariance matrix under two-step monotone incomplete sample. The maximum likelihood estimator of the mean vector is unbiased but that of the covariance matrix is biased. We derive an unbiased estimator for the covariance matrix using some fundamental properties of the Wishart matrix. The properties of the estimators are investigated and the accuracies are checked by a numerical simulation.

Asymptotic expansion for distribution of the trace of a covariance matrix under a two-step monotone incomplete sample

The covariance matrix is embedded in several statistics (such as the trace and general variance) of multivariate statistical analysis. We investigate the trace of the covariance matrix in the context of a two-step monotone incomplete sample drawn from Np+q(μ,Σ), a multivariate normal population with mean μ and covariance matrix Σ. Since there are the maximum likelihood estimator (MLE) and the unbiased estimator (UBE) for the covariance matrix, we uniformly deal with these and derive the asymptotic distribution and the asymptotic expansion of the distribution of the trace using them. The accuracy of these results is investigated by numerical simulation, which may be applicable to multivariate analysis under the two-step monotone incomplete sample.