Differential equation models for statistical functions

Differential equations have been used in statistics to define functions such as probability densities. But the idea of using differential equation formulations of stochastic models has a much wider scope. The author gives several examples, including simultaneous estimation of a regression model and residual density, monotone smoothing, specification of a link function, differential equation models of data, and smoothing over complicated multidimensional domains. This paper aims to stimulate interest in this approach to functional estimation problems, rather than provide carefully worked out methods.     

Bayesian prediction of waiting times in stochastic models

The authors show how saddlepoint techniques lead to highly accurate approximations for Bayesian predictive densities and cumulative distribution functions in stochastic model settings where the prior is tractable, but not necessarily the likelihood or the predictand distribution. They consider more specifically models involving predictions associated with waiting times for semi‐Markov processes whose distributions are indexed by an unknown parameter θ. Bayesian prediction for such processes when they are not stationary is also addressed and the inverse‐Gaussian based saddlepoint approximation of Wood, Booth & Butler (1993) is shown to accurately deal with the nonstationarity whereas the normal‐based Lugannani & Rice (1980) approximation cannot, Their methods are illustrated by predicting various waiting times associated with M/M/q and M/G/1 queues. They also discuss modifications to the matrix renewal theory needed for computing the moment generating functions that are used in the saddlepoint methods.     

Rate efficient estimation of realized Laplace transform of volatility with microstructure noise

In this paper, we consider the problem of estimating the Laplace transform of volatility within a fixed time interval [0,T] using high‐frequency sampling, where we assume that the discretized observations of the latent process are contaminated by microstructure noise. We use the pre‐averaging approach to deal with the effect of microstructure noise. Under the high‐frequency scenario, we obtain a consistent estimator whose convergence rate is , which is known as the optimal convergence rate of the estimation of integrated volatility functionals under the presence of microstructure noise. The related central limit theorem is established. The simulation studies justify the finite‐sample performance of the proposed estimator.     

Extension of the Application of Conway‐Maxwell‐Poisson Models: Analyzing Traffic Crash Data Exhibiting Underdispersion

The objective of this article is to evaluate the performance of the COM‐Poisson GLM for analyzing crash data exhibiting underdispersion (when conditional on the mean). The COM‐Poisson distribution, originally developed in 1962, has recently been reintroduced by statisticians for analyzing count data subjected to either over‐ or underdispersion. Over the last year, the COM‐Poisson GLM has been evaluated in the context of crash data analysis and it has been shown that the model performs as well as the Poisson‐gamma model for crash data exhibiting overdispersion. To accomplish the objective of this study, several COM‐Poisson models were estimated using crash data collected at 162 railway‐highway crossings in South Korea between 1998 and 2002. This data set has been shown to exhibit underdispersion when models linking crash data to various explanatory variables are estimated. The modeling results were compared to those produced from the Poisson and gamma probability models documented in a previous published study. The results of this research show that the COM‐Poisson GLM can handle crash data when the modeling output shows signs of underdispersion. Finally, they also show that the model proposed in this study provides better statistical performance than the gamma probability and the traditional Poisson models, at least for this data set.     

Involvement of Ministries of Health in Health Service Coverage Decisions: Is England an Aberrant Case?

This article examines the involvement of ministries of health in making health service coverage decisions in Denmark, England, France and Germany. The study aims to inform debate in England about the feasibility of reducing perceived ministerial and bureaucratic ‘interference’ in decisions affecting the National Health Service, based on interviews with senior government officials and other health system stakeholders. Ministries of health differ in their involvement in health system governance and coverage decisions (‘the benefits package’), reflecting differences in institutional arrangements. In all four countries, organizations at arm's length or independent from government are either involved in providing technical advice to the ministry of health or have been mandated to take these decisions themselves. However, ministries of health occasionally intervene in the decision‐making process or ignore the advice of these organizations. The Department of Health in England is not an aberrant case, at least in relation to coverage decisions. Indeed, ministries of health in Denmark and France play a larger role in making these decisions. Public pressure, often amplified by the media, is a shared reason for ministerial and ministry involvement in all four countries. This dynamic may thus limit the feasibility of attempts to further separate the NHS from both the Department of Health and wider political pressures.     

Peer Victimization,Self‐esteem,and Ego Resilience Types in Adolescents: A Prospective Analysis of Person‐context Interactions

This study examined bidirectional, longitudinal associations between peer victimisation and self‐esteem in adolescents, and tested for moderator effects of undercontrolling, overcontrolling, and ego‐resilient personality types in these associations. Data were used from 774 adolescents ages 11–16 years who participated in a three‐wave (i.e., 2005, 2006, and 2007) longitudinal study. Structural equation modelling analyses in Mplus demonstrated that, controlling for earlier levels of self‐esteem, self‐reported peer victimization was associated with lower self‐esteem across one‐year time intervals. Vice versa, however, low self‐esteem was not predictive of subsequent self‐reported victimization. Evidence was also found for a moderator effect of personality type on the longitudinal associations between self‐esteem and victimization. Only in the subgroup of overcontrolling adolescents was lower self‐esteem related to subsequently higher levels of peer victimization; their undercontrolling and ego‐resilient peers were unaffected.     

Japanese and American Children's Reasoning about Accepting Credit for Prosocial Behavior

Children's reasoning about the appropriateness of accepting credit for one's own prosocial behavior was examined. Participants aged 7–11 years old in Japan and the USA (total N = 206) were presented with a series of stories in which a protagonist performs a good deed and is asked about it by another character. Across stories, the protagonist either truthfully acknowledges the deed or falsely denies it, in a statement that is made either in public or in private, and is addressed to either a teacher or to a peer. As predicted, Japanese children judged protagonists less favorably when they acknowledged the good deed in public rather than in private. Further, Japanese children tended to view modest lies more favorably overall than did children in the USA. These results point to the importance of modesty in Japan and to the ways in which Japanese children take into account the social context of communication when deciding whether it is appropriate for individuals to convey information about themselves.     

Effects of a Punitive Environment on Children's Executive Functioning: A Natural Experiment

Few studies have examined the influence of environmental factors on children's executive functioning (EF) performance. The present study examined the effects of a punitive vs. non‐punitive school environment on West African children's EF skills. Tasks included a ‘cool’ (relatively non‐affective) and ‘hot’ (relatively affective/motivational) version of three EF tasks: delay of gratification; gift delay; and dimensional change card sort. Children had more difficulties with the hot versions of the tasks than the cool versions, and older children outperformed younger children. After controlling for verbal ability (Peabody picture vocabulary test‐third edition), a consistent pattern of interaction between school and grade level emerged. Overall, kindergarten children in the punitive school performed no differently than their counterparts in the non‐punitive school. However, in grade 1, children in the punitive school performed significantly worse than their counterparts in the non‐punitive school. These results point to the need to consider interactions among discipline style, age, and internalization processes of self‐regulation to better understand environmental influences on EF development.     

A longitudinal study of depressiveness in children in public care

Rajhvajn Bulat L. A longitudinal study of depressiveness in children in public care Int J Soc Welfare 2010: 19: 412–423 © 2009 The Author, Journal compilation © 2009 Blackwell Publishing Ltd and the International Journal of Social Welfare. The aim of this article is to analyse the challenges involved when making longitudinal observations of depressiveness in children raised in public care. The first measurement comprised 375 children from children's homes and foster families; however, most of the results are based on an analysis of the 139 children who participated in both parts of the research. We used the Child Depression Inventory and the anxiety/depression subscales of Youth Self Report and Child Behaviour Checklist as measures of depressiveness. The comparison of results from the first and second measurements showed that depressiveness in children in public care decreased over time. Children who grew up in children homes were, in the first measurement, more depressed than those living in foster families, but after five years that difference had disappeared. Furthermore, decrease in depressiveness is predominantly associated with less frequent delinquent, aggressive or hyperactive behaviour, less withdrawal and better control over uncomfortable emotions.     

Attenuating Initial Beliefs: Increasing the Acceptance of Anthropogenic Climate Change Information by Reflecting on Values

Anthropogenic climate change information tends to be interpreted against the backdrop of initial environmental beliefs, which can lead to some people being resistant toward the information. In this article (N = 88), we examined whether self‐affirmation via reflection on personally important values could attenuate the impact of initial beliefs on the acceptance of anthropogenic climate change evidence. Our findings showed that initial beliefs about the human impact on ecological stability influenced the acceptance of information only among nonaffirmed participants. Self‐affirmed participants who were initially resistant toward the information showed stronger beliefs in the existence of climate change risks and greater acknowledgment that individual efficacy has a role to play in reducing climate change risks than did their nonaffirmed counterparts.