We give a general matrix formula for computing the bias of the exact unconditional maximum likelihood estimate in ARMA models, with known and unknown mean, up to order 1/n, where n is the length of the series. Some illustrative examples are presented.

Under suitable regularity conditions, an appropriate improved score statistic was derived recently by Cordeiro and Ferrari (1991). In the spirit of their work, this paper discusses how in practice we can obtain improved score statistics in exponential family nonlinear models. Some formulae for...

A rigorous asymptotic theory for Pearson residuals in generalized linear models is not yet available. We give matrix formulae of order n-1, where n is the sample size, for the first two moments of these residuals. The formulae are applicable to many regression models in common use. We suggest...

Under suitable regularity conditions, an improved score test was derived by Cordeiro and Ferrari (1991). The test is based on a corrected score statistic which has a chi-squared distribution to order n-1 under the null hypothesis, where n is the sample size. In this paper we follow their...

This paper gives a general Bartlett correction formula to improve likelihood ratio tests in heteroskedastic t regression models where both location and dispersion parameters vary with the observations. The correction covers many important and commonly used models and can be viewed as an...

In this paper, we derive general formulae for second-order biases of maximum likelihood estimates in overdispersed generalized linear models, thus generalizing results by Cordeiro and McCullagh (J. Roy. Statist. Soc. Ser. B 53 (1991) 629), and Botter and Cordeiro (Statist. Comput. Simul. 62...

In this paper, we formulate a flexible density function from the selection mechanism viewpoint (see, for example, Bayarri and DeGroot (1992) and Arellano-Valle et al. (2006)) which possesses nice biological and physical interpretations. The new density function contains as special cases many...

In this article, for the first time, we propose the negative binomial--beta Weibull (BW) regression model for studying the recurrence of prostate cancer and to predict the cure fraction for patients with clinically localized prostate cancer treated by open radical prostatectomy. The cure model...

The modeling and analysis of lifetimes is an important aspect of statistical work in a wide variety of scientific and technological fields. For the first time, the so-called generalized exponential geometric distribution is introduced. The new distribution can have a decreasing, increasing and...

For the first time, we propose the so-called beta generalized half-normal distribution, which contains some important distributions as special cases, such as the half-normal and generalized half-normal (Cooray and Ananda, 2008) distributions. We derive expansions for the cumulative distribution...