The Bartlett-type adjustment is a higher-order asymptotic method for reducing the errors of the chi-squared approximations to the null distributions of various test statistics, which ensures that the resulting test has size α+o(N−1), where 0α1 is the significance level and N is the sample...

This paper addresses, for a composite hypothesis about a subvector of the parameters in the parametric model, the issues posed by Rao and Mukerjee (1995) [22] and Li (2001) [14] on the power under a sequence of local alternatives. It is shown that a partially adjusted test statistic in a class...

The Bartlett-type adjustment is a higher-order asymptotic method for improving the chi-squared approximation to the null distributions of various test statistics. Though three influential papers were published in 1991—Chandra and Mukerjee (1991) [8], Cordeiro and Ferrari (1991) [12] and...

The purpose of this paper is to investigate the effect of nonnormality upon the nonnull distributions of some MANOVA test statistics under normality. It is shown that whatever the underlying distributions, the difference of the local powers up to order N-1 (N is the total number of observations)...

The purpose of this paper is, in multivariate linear regression model (Part I) and GMANOVA model (Part II), to investigate the effect of nonnormality upon the nonnull distributions of some multivariate test statistics under normality. It is shown that whatever the underlying distributions, the...

An asymptotic expansion of the distribution of Student's t type statistic based on the multivariate standardized or studentized sample mean vector is obtained by making use of an Edgeworth expansion up to the order O(N-2), where N is sample size and Student's t type transformation is defined by...

A closed-form expression for the exponential rate of an estimator in the Gaussian AR(1) process is obtained. This shows that the exponential rates of several famous estimators are all identical. Further it is shown that mean-correction does not affect the large deviation asymptotics.

Statistical inference for stationary time series is often based on the maximum likelihood principle, i.e., the maximization of the (quasi) likelihood of observations derived on Gaussian assumptions, although no such distributional assumptions are made. In this paper, we define the disparity...

Moderate deviations limit theorem is proved for quadratic forms in zero-mean Gaussian stationary processes. Two particular cases are the cumulative periodogram and the kernel spectral density estimator. We also derive the exponential decay of moderate deviation probabilities of goodness-of-fit...