Trend estimation of multivariate time series with controlled smoothness

This paper extends the univariate time series smoothing approach provided by penalized least squares to a multivariate setting, thus allowing for joint estimation of several time series trends. The theoretical results are valid for the general multivariate case, but particular emphasis is placed on the bivariate situation from an applied point of view. The proposal is based on a vector signal-plus-noise representation of the observed data that requires the first two sample moments and specifying only one smoothing constant. A measure of the amount of smoothness of an estimated trend is introduced so that an analyst can set in advance a desired percentage of smoothness to be achieved by the trend estimate. The required smoothing constant is determined by the chosen percentage of smoothness. Closed form expressions for the smoothed estimated vector and its variance-covariance matrix are derived from a straightforward application of generalized least squares, thus providing best linear unbiased estimates for the trends. A detailed algorithm applicable for estimating bivariate time series trends is also presented and justified. The theoretical results are supported by a simulation study and two real applications. One corresponds to Mexican and US macroeconomic data within the context of business cycle analysis, and the other one to environmental data pertaining to a monitored site in Scotland.     

Characterization of Lindley distribution by truncated moments

In the past few years, the Lindley distribution has gained popularity for modeling lifetime data as an alternative to the exponential distribution. This paper provides two new characterizations of the Lindley distribution. The first characterization is based on a relation between left truncated moments and failure rate function. The second characterization is based on a relation between right truncated moments and reversed failure rate function.     

Gamma-Maxwell distribution

A new two-parameter distribution, the gamma-Maxwell distribution, isproposed and studied. We generate the new distribution using the gamma-G generator of distributions. The proposal distribution can be seen as an extension of the Maxwell distribution with more flexibility in terms of the distribution asymmetry and kurtosis. We study some probability properties, discuss maximum-likelihood estimation and present a real data application indicating that the new distribution can improve the ordinary Maxwell distribution in fitting real data.     

Generalized Kerridge’s inaccuracy measure for conditionally specified models

Recently, conditional Renyi’s divergence of order α and Kerridge’s inaccuracy measures are studied by Navarro et al. (2014 Navarro, J., Sunoj, S.M., Linu, M.N. (2014). Characterizations of bivariate models using some dynamic conditional information divergence measures. Commun. Stat. Theory Methods 43:1939–1948.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]). In the present article, a generalized dynamic conditional Kerridge’s inaccuracy measure is introduced, which can be represented as the sum of conditional Renyi’s divergence and Renyi’s entropy. Some useful bounds are obtained using the concept of likelihood ratio order. The results are extended to weighted distributions. Sufficient conditions are obtained for the monotonicity of the proposed measure. Characterizations for bivariate exponential conditional distribution are presented based on the proposed measure.     

Application of an imputation method for variance estimation under pseudo-likelihood when missing data are NMAR

When data are outcome-dependent non response, pseudo-likelihood yields consistent regression coefficients without specifying the missing data mechanism. However, it is onerous to derive parameter estimators including their standard errors from the regression coefficients under pseudo-likelihood (PL). The present study applies an imputation method to compute the asymptotic standard errors of parameter estimators. The proposed method is simpler than Delta method and it showed similar effect size of the standard errors to bootstrapping in simulation and application studies.     

Dynamic version of weighted cumulative residual entropy

Some extensions of Shannon entropy to the survival function have been recently proposed. Misagh et al. (2011 Misagh, F., Panahi, Y., Yari, G.H., Shahi, R. (2011, September). Weighted cumulative entropy and its estimation. In: Quality and Reliability (ICQR), 2011, IEEE International conference (pp. 477–480), IEEE.[Crossref] , [Google Scholar]) introduced weighted cumulative residual entropy (WCRE) that was studied more by Mirali et al. (2015 Mirali, M., Baratpour, S., Fakoor, V. (2015). On weighted cumulative residual entropy. Commun. Stat. Theory Methods. doi:10.1080103610926.2015.1053932.[Web of Science ®] , [Google Scholar]). In this article, the dynamic version of WCRE is proposed. Some relationships of this measure with well-known reliability measures and ageing classes are studied and some characterization results for exponential and Rayleigh distributions are provided. Also, a non parametric estimation of dynamic version of WCRE is introduced and its asymptotic behavior is investigated.     

Bayesian quantile regression for skew-normal linear mixed models

Linear mixed models have been widely used to analyze repeated measures data which arise in many studies. In most applications, it is assumed that both the random effects and the within-subjects errors are normally distributed. This can be extremely restrictive, obscuring important features of within-and among-subject variations. Here, quantile regression in the Bayesian framework for the linear mixed models is described to carry out the robust inferences. We also relax the normality assumption for the random effects by using a multivariate skew-normal distribution, which includes the normal ones as a special case and provides robust estimation in the linear mixed models. For posterior inference, we propose a Gibbs sampling algorithm based on a mixture representation of the asymmetric Laplace distribution and multivariate skew-normal distribution. The procedures are demonstrated by both simulated and real data examples.     

Goodness-of-fit tests based on Verma Kullback–Leibler information

In this article, a new consistent estimator of Veram’s entropy is introduced. We establish the entropy test based on the new information namely Verma Kullback–Leibler discrimination methodology. The results are used to introduce goodness-of-fit tests for normal and exponential distributions. The root of mean square errors, critical values, and powers for some alternatives are obtained by simulation. The proposed test is compared with other tests.     

Elements of cultural competence in an Australian Aboriginal maternity program

Background

Pregnancy, labour and neonatal health outcomes for Australian Aboriginal women and their infants are frequently worse than those of the general population. Provision of culturally competent services may reduce these differences by improving access to timely and regular antenatal care. In an effort to address these issues, the Aboriginal Maternity Group Practice Program commenced in south metropolitan Perth, Western Australia, in 2011. The program employed Aboriginal Grandmothers, Aboriginal Health Officers and midwives working in a partnership model with pre-existing maternity services in the area.