In this paper the asymptotic behavior of an unstable integer-valued autoregressive model of order p (INAR( p)) is described. Under a natural assumption it is proved that the sequence of appropriately scaled random step functions formed from an unstable INAR( p) process converges weakly towards a squared Bessel process. We note that this limit behavior is quite different from that of familiar unstable autoregressive processes of order p. An application for Boston armed robberies data set is presented.
Environmental epidemiological studies of the health effects of air pollution frequently utilize the generalized additive model (GAM) as the standard statistical methodology, considering the ambient air pollutants as explanatory covariates. Although exposure to air pollutants is multi‐dimensional, the majority of these studies consider only a single pollutant as a covariate in the GAM model. This model restriction may be because the pollutant variables do not only have serial dependence but also interdependence between themselves. In an attempt to convey a more realistic model, we propose here the hybrid generalized additive model–principal component analysis–vector auto‐regressive (GAM–PCA–VAR) model, which is a combination of PCA and GAMs along with a VAR process. The PCA is used to eliminate the multicollinearity between the pollutants whereas the VAR model is used to handle the serial correlation of the data to produce white noise processes as covariates in the GAM. Some theoretical and simulation results of the methodology proposed are discussed, with special attention to the effect of time correlation of the covariates on the PCA and, consequently, on the estimates of the parameters in the GAM and on the relative risk, which is a commonly used statistical quantity to measure the effect of the covariates, especially the pollutants, on population health. As a main motivation to the methodology, a real data set is analysed with the aim of quantifying the association between respiratory disease and air pollution concentrations, especially particulate matter PM10, sulphur dioxide, nitrogen dioxide, carbon monoxide and ozone. The empirical results show that the GAM–PCA–VAR model can remove the auto‐correlations from the principal components. In addition, this method produces estimates of the relative risk, for each pollutant, which are not affected by the serial correlation in the data. This, in general, leads to more pronounced values of the estimated risk compared with the standard GAM model, indicating, for this study, an increase of almost 5.4% in the risk of PM10, which is one of the most important pollutants which is usually associated with adverse effects on human health.
Data harmonization is a topic of growing importance to demographers, who increasingly conduct domestic or international comparative research. Many self-reported survey items cannot be directly compared across demographic groups or countries because these groups differ in how they use subjective response categories. Anchoring vignettes, already appearing in numerous surveys worldwide, promise to overcome this problem. However, many anchoring vignettes have not been formally evaluated for adherence to the key measurement assumptions of vignette equivalence and response consistency. This article tests these assumptions in some of the most widely fielded anchoring vignettes in the world: the health vignettes in the World Health Organization (WHO) Study on Global AGEing and Adult Health (SAGE) and World Health Survey (WHS) (representing 10 countries; n = 52,388), as well as similar vignettes in the Health and Retirement Study (HRS) (n = 4,528). Findings are encouraging regarding adherence to response consistency, but reveal substantial violations of vignette equivalence both cross-nationally and across socioeconomic groups. That is, members of different sociocultural groups appear to interpret vignettes as depicting fundamentally different levels of health. The evaluated anchoring vignettes do not fulfill their promise of providing interpersonally comparable measures of health. Recommendations for improving future implementations of vignettes are discussed.
The first-order integer-valued autoregressive (INAR(1)) process is investigated, where the autoregressive coefficient is close to one. It is shown that the limiting distribution of the conditional least-squares estimator for this coefficient is normal and, in contrast to the familiar AR(1) process, the rate of convergence is n 3/2 . Finally, the nearly critical Galton-Watson process with unobservable immigration is discussed.
Smart cities offer services to their inhabitants which make everyday life easier beyond providing a feedback channel to the city administration. For instance, a live timetable service for public transportation or real-time traffic jam notification can increase the efficiency of travel planning substantially. Traditionally, the implementation of these smart city services require the deployment of some costly sensing and tracking infrastructure. As an alternative, the crowd of inhabitants can be involved in data collection via their mobile devices. This emerging paradigm is called mobile crowd-sensing or participatory sensing. In this paper, we present our generic framework built upon XMPP (Extensible Messaging and Presence Protocol) for mobile participatory sensing based smart city applications. After giving a short description of this framework we show three use-case smart city application scenarios, namely a live transit feed service, a soccer intelligence agency service and a smart campus application, which are currently under development on top of our framework.
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