Higher-order moments,cumulants and spectral densities of the NGINAR(1) process

The motivation for time series with geometric marginal distributions arises from noting that the Poisson distribution is not always suitable for the modeling and analysis of integer-valued time series. The NGINAR(1) process that has been introduced by Risti? et al. (2009) represents a class of such time series. Joint higher-order (factorial) moments and cumulants with some other related statistical measures of the NGINAR(1) process are constructed. Also, the spectral and bispectral density functions of this process are investigated, including their nonparametric estimators, using the multitapering method. A real data example of the nonparametric multitaper spectral estimates is investigated, with a discussion of the results obtained.     

Influence diagnostics in a multivariate normal regression model with general parameterization

Patriota and Lemonte [24] introduced a quite general multivariate normal regression model. This model considers that the mean vector and the covariance matrix share the same vector of parameters. In this paper we present some influence assessment for this model, such as the local influence, total local influence of an individual and generalized leverage which are discussed. Additionally, the normal curvatures for local influence studies are derived under some perturbation schemes.     

Performance of the empirical Bayes estimator for fixed parameters

When the unbiased estimators of a set of parameters are independently and normally distributed, the Empirical Bayes Estimator (EB) for each of the parameters depends on all the parameters. When these parameters are considered to be fixed, Rao and Shinozaki (1978) [7] compared the mean square error (MSE) of this estimator for an individual parameter with the variance of its unbiased estimator, and cautioned that its bias may be large. In this article, the conditions required for (a) the MSE of the EB to be smaller than the variance of the unbiased estimator and (b) at the same time, for its bias to be smaller than a specified fraction of the square root of the MSE are evaluated. To satisfy these conditions, critical limits for the difference of the parameter from the average of all the parameters and the sum of such differences over all the parameters are determined. As an illustration, for the daily inpatient hospital expenses in the Metropolitan Statistical Areas (MSAs) of 15 states in the US, the sample means and EBs are compared through the estimates of these limits.     

Inflated beta distributions

This paper considers the issue of modeling fractional data observed on [0,1), (0,1] or [0,1]. Mixed continuous-discrete distributions are proposed. The beta distribution is used to describe the continuous component of the model since its density can have quite different shapes depending on the values of the two parameters that index the distribution. Properties of the proposed distributions are examined. Also, estimation based on maximum likelihood and conditional moments is discussed. Finally, practical applications that employ real data are presented.     

A note on the mean past and the mean residual life of a (n − k + 1)-out-of-n system under multi monitoring

In the study of the reliability of technical systems, k-out-of-n systems play an important role. In the present paper, we consider a (n − k + 1)-out-of-n system consisting of n identical components such that the lifetimes of components are independent and have a common distribution function F. It is assumed that the number of monitoring is l and the total number of failures of the components at time t _i is m _i , i = 1, . . . , l − 1. Also at time t _l (t ₁ < . . . < t _l ) the system have failed or the system is still working. Under these conditions, the mean past lifetime, the mean residual lifetime of system and their properties are investigated.     

The behavioural wedge

When nations fail to agree, can individual citizens make a difference? The third of our post-Copenhagen features is by Jonathan Gilligan, Thomas Dietz, Gerald T. Gardner, Paul C. Stern , and Michael P. Vandenbergh . They look at the effects that voluntary actions by individuals can have, and at the policies that can best encourage such actions.     

BAYESIAN HIDDEN MARKOV MODELS FOR LONGITUDINAL COUNTS

This paper describes a Bayesian approach to modelling carcinogenity in animal studies where the data consist of counts of the number of tumours present over time. It compares two autoregressive hidden Markov models. One of them models the transitions between three latent states: an inactive transient state, a multiplying state for increasing counts and a reducing state for decreasing counts. The second model introduces a fourth tied state to describe non‐zero observations that are neither increasing nor decreasing. Both these models can model the length of stay upon entry of a state. A discrete constant hazards waiting time distribution is used to model the time to onset of tumour growth. Our models describe between‐animal‐variability by a single hierarchy of random effects and the within‐animal variation by first‐order serial dependence. They can be extended to higher‐order serial dependence and multi‐level hierarchies. Analysis of data from animal experiments comparing the influence of two genes leads to conclusions that differ from those of Dunson (2000). The observed data likelihood defines an information criterion to assess the predictive properties of the three‐ and four‐state models. The deviance information criterion is appropriately defined for discrete parameters.     

MAXIMUM LIKELIHOOD ESTIMATION FOR A POISSON RATE PARAMETER WITH MISCLASSIFIED COUNTS

This paper proposes a Poisson‐based model that uses both error‐free data and error‐prone data subject to misclassification in the form of false‐negative and false‐positive counts. It derives maximum likelihood estimators (MLEs) for the Poisson rate parameter and the two misclassification parameters — the false‐negative parameter and the false‐positive parameter. It also derives expressions for the information matrix and the asymptotic variances of the MLE for the rate parameter, the MLE for the false‐positive parameter, and the MLE for the false‐negative parameter. Using these expressions the paper analyses the value of the fallible data. It studies characteristics of the new double‐sampling rate estimator via a simulation experiment and applies the new MLE estimators and confidence intervals to a real dataset.     

ADDITIVE MODELS WITH PREDICTORS SUBJECT TO MEASUREMENT ERROR

This paper develops a likelihood‐based method for fitting additive models in the presence of measurement error. It formulates the additive model using the linear mixed model representation of penalized splines. In the presence of a structural measurement error model, the resulting likelihood involves intractable integrals, and a Monte Carlo expectation maximization strategy is developed for obtaining estimates. The method's performance is illustrated with a simulation study.     

Asymptotic bias in the linear mixed effects model under non-ignorable missing data mechanisms

Summary.  In longitudinal studies, missingness of data is often an unavoidable problem. Estimators from the linear mixed effects model assume that missing data are missing at random. However, estimators are biased when this assumption is not met. In the paper, theoretical results for the asymptotic bias are established under non-ignorable drop-out, drop-in and other missing data patterns. The asymptotic bias is large when the drop-out subjects have only one or no observation, especially for slope-related parameters of the linear mixed effects model. In the drop-in case, intercept-related parameter estimators show substantial asymptotic bias when subjects enter late in the study. Eight other missing data patterns are considered and these produce asymptotic biases of a variety of magnitudes.