Parameter estimation for switched counting processes

The paper investigates parameter estimation problems in special Markov modulated counting processes. The events occuring at any state of an underlying Markov chain can be equipped with marks performing additional information on the events. Specifying the model to the case of two-state Markov chain modulation, the so-called switched counting process, some statistical problems are studied:maximum likelihood estimators, Rao-Blackwell optimal estimators, test of equality of the counting intensities of the two states and minimax estimation procedures. Tne consideration could be applied in various practical problems, in particular, in queueing and in reliability models, for example in failure-repair processes with alternatively operating repair systems.     

On multiple constraint skewed models

The Azzalini [A. Azzalini, A class of distributions which includes the normal ones, Scandi. J. Statist. 12 (1985), pp. 171–178.] skew normal model can be viewed as one involving normal components subject to a single linear constraint. As a natural extension of this model, we discuss skewed models involving multiple linear and nonlinear constraints and possibly non-normal components. Particular attention is devoted to a distribution called the extended two-piece normal (ETN) distribution. This model is a two-constraint extension of the two-piece normal model introduced by Kim [H.J. Kim, On a class of two-piece skew normal distributions, Statistics 39(6) (2005), pp. 537–553.]. Likelihood inference for the ETN distribution is developed and illustrated using two data sets.     

Non-negative estimation of variance components in heteroscedastic one-way random-effects ANOVA models

There is a considerable amount of literature dealing with inference about the parameters in a heteroscedastic one-way random-effects ANOVA model. In this paper, we primarily address the problem of improved quadratic estimation of the random-effect variance component. It turns out that such estimators with a smaller mean squared error compared with some standard unbiased quadratic estimators exist under quite general conditions. Improved estimators of the error variance components are also established.     

A bivariate density estimation method based on level crossings

This article introduces a method of nonparametric bivariate density estimation based on a bivariate sample level crossing function, which leads to the construction of a bivariate level crossing empirical distribution function (BLCEDF). An efficiency function for this BLCEDF relative to the classical empirical distribution function (EDF), is derived. The BLCEDF gives more efficient estimates than the EDF in the tails of any underlying continuous distribution, for both small and large sample sizes. On the basis of BLCEDF we define a bivariate level crossing kernel density estimator (BLCKDE) and study its properties. We apply the BLCEDF and BLCKDE for various distributions and provide results of simulations that confirm the theoretical properties. A real-world example is given.     

Some characterization results for parallel systems with two heterogeneous exponential components

In this paper, we study ordering properties of lifetimes of parallel systems with two independent heterogeneous exponential components in terms of the likelihood ratio order (reversed hazard rate order) and the hazard rate order (stochastic order). We establish, among others, that the weakly majorization order between two hazard rate vectors is equivalent to the likelihood ratio order (reversed hazard rate order) between lifetimes of two parallel systems, and that the p-larger order between two hazard rate vectors is equivalent to the hazard rate order (stochastic order) between lifetimes of two parallel systems. Moreover, we extend the results to the proportional hazard rate models. The results derived here strengthen and generalize some of the results known in the literature.     

A new unrelated question randomized response model

In this paper, we extend the work of Gjestvang and Singh [A new randomized response model, J. R. Statist. Soc. Ser. B (Methodological) 68 (2006), pp. 523–530] to propose a new unrelated question randomized response model that can be used for any sampling scheme. The interesting thing is that the estimator based on one sample is free from the use of known proportion of an unrelated character, unlike Horvitz et al. [The unrelated question randomized response model, Social Statistics Section, Proceedings of the American Statistical Association, 1967, pp. 65–72], Greenberg et al. [The unrelated question randomized response model: Theoretical framework, J. Amer. Statist. Assoc. 64 (1969), pp. 520–539] and Mangat et al. [An improved unrelated question randomized response strategy, Calcutta Statist. Assoc. Bull. 42 (1992), pp. 167–168] models. The relative efficiency of the proposed model with respect to the existing competitors has been studied.     

On a bounded bimodal two-sided distribution fitted to the Old-Faithful geyser data

In this paper, we shall develop a novel family of bimodal univariate distributions (also allowing for unimodal shapes) and demonstrate its use utilizing the well-known and almost classical data set involving durations and waiting times of eruptions of the Old-Faithful geyser in Yellowstone park. Specifically, we shall analyze the Old-Faithful data set with 272 data points provided in Dekking et al. [3]. In the process, we develop a bivariate distribution using a copula technique and compare its fit to a mixture of bivariate normal distributions also fitted to the same bivariate data set. We believe the fit-analysis and comparison is primarily illustrative from an educational perspective for distribution theory modelers, since in the process a variety of statistical techniques are demonstrated. We do not claim one model as preferred over the other.     

A Markov regime‐switching model for crude‐oil markets: Comparison of composite likelihood and full likelihood

We use the two‐state Markov regime‐switching model to explain the behaviour of the WTI crude‐oil spot prices from January 1986 to February 2012. We investigated the use of methods based on the composite likelihood and the full likelihood. We found that the composite‐likelihood approach can better capture the general structural changes in world oil prices. The two‐state Markov regime‐switching model based on the composite‐likelihood approach closely depicts the cycles of the two postulated states: fall and rise. These two states persist for on average 8 and 15 months, which matches the observed cycles during the period. According to the fitted model, drops in oil prices are more volatile than rises. We believe that this information can be useful for financial officers working in related areas. The model based on the full‐likelihood approach was less satisfactory. We attribute its failure to the fact that the two‐state Markov regime‐switching model is too rigid and overly simplistic. In comparison, the composite likelihood requires only that the model correctly specifies the joint distribution of two adjacent price changes. Thus, model violations in other areas do not invalidate the results. The Canadian Journal of Statistics 41: 353–367; 2013 © 2013 Statistical Society of Canada