The nominal response model (NRM) was proposed by Bock [Psychometrika 37 (1972) 29–51] in order to improve the latent trait (ability) estimation in multiple choice tests with nominal items. When the item parameters are known, expectation a posteriori or maximum a posteriori methods are commonly employed to estimate the latent traits, considering a standard symmetric normal distribution as the latent traits prior density. However, when this item set is presented to a new group of examinees, it is not only necessary to estimate their latent traits but also the population parameters of this group. This article has two main purposes: first, to develop a Monte Carlo Markov Chain algorithm to estimate both latent traits and population parameters concurrently. This algorithm comprises the Metropolis–Hastings within Gibbs sampling algorithm (MHWGS) proposed by Patz and Junker [Journal of Educational and Behavioral Statistics 24 (1999b) 346–366]. Second, to compare, in the latent trait recovering, the performance of this method with three other methods: maximum likelihood, expectation a posteriori and maximum a posteriori. The comparisons were performed by varying the total number of items (NI), the number of categories and the values of the mean and the variance of the latent trait distribution. The results showed that MHWGS outperforms the other methods concerning the latent traits estimation as well as it recoveries properly the population parameters. Furthermore, we found that NI accounts for the highest percentage of the variability in the accuracy of latent trait estimation.

In this article we compute three corrected score statistic versions: the Bartlett-type correction and the monotone corrected score statistics proposed by Kakizawa [Biometrika 83 (1996) 923–927] and Cordeiro, Ferrari and Cysneiros [J. Stat. Comput. Simul. 62 (1998) 123–136]. These corrected statistics are used to test the null hypothesis concerning some parameter of interest of an ARMA model, assumed to be Gaussian, stationary and invertible. We also consider the situations where nuisance parameters are present. The formulas are written in matrix form, appropriate for the use of symbolic or numerical languages. Some simulation results are also presented for the AR(1), MA(1) and ARMA(1, 1) models.

The poverty analysis may require the observation of the same set of households over the time in order to explain the evolution of the poverty situation and to try to explain their behavior. In this case, the poverty measures have to be determined continuously in some interval [0, T] and the sample poverty index becomes time-dependent. In this paper, we settle the global problem of the weak convergence of the time-dependent poverty measures in the functional space of continuous functions defined on [0, T]. We entirely describe the uniform asymptotic normality of the class of nonweighted poverty indices including the Foster–Greer–Thorbecke and Chakravarty ones, which both have the special property of satisfying all the needed axioms for a poverty index.

We consider the problem of estimation of density function by the method of delta sequences for functional data with values in an infinite dimensional separable Banach space.

A workload model using the infinite source Poisson model for bursts is combined with the on–off model for within burst activity. Burst durations and on–off durations are assumed to have heavy-tailed distributions with infinite variance and finite mean. Since the number of bursts is random, one can consider limiting results based on “random centering” of a random sum for the total workload from all sources. Convergence results are shown to depend on the tail indices of both the on–off durations and the lifetimes distributions. Moreover, the results can be separated into cases depending on those tail indices. In one case where all distributions are heavy tailed it is shown that the limiting result is Brownian motion. In another case, convergence to fractional Brownian motion is shown, where the Hurst parameter depends on the heavy-tail indices of the distribution of the on, off and burst durations.

R-processes are a new type of discrete stationary stochastic process which we have recently shown to be finitarily isomorphic to Bernoulli schemes. Here, we present a simple example of an r-process and compute its entropy. Then, we prove that r-processes are weak Bernoulli.

In this note we deal with a panel data model with fixed effects. We show that a Bayesian procedure based on the reference prior suffers from the incidental parameter problem, as also happens with the Jeffrey’s prior [Econom. Lett. 82 (2004) 135–138]. Using an alternative prior distribution we present a solution to the problem.