The conditional cumulative distribution function in single functional index model

ABSTRACT

We consider the estimation of the conditional cumulative distribution function of a scalar response variable Y given a Hilbertian random variable X when the observations are linked via a single-index structure. We establish the pointwise and the uniform almost complete convergence (with the rate) of the kernel estimate of this model. As an application, we show how our result can be applied in the prediction problem via the conditional median estimate. Also, the choice of the functional index via the cross-validation procedure is also discussed but not attacked.     

Minimal Neighbor Designs in Linear Blocks

Neighbor designs are useful to neutralize the neighbor effects. In literature, most of the constructed neighbor designs are in circular blocks but linear blocks have more practical application in field experiments. In this article, some infinite series of minimal neighbor designs are constructed in proper linear blocks. There are many situations where minimal neighbor designs cannot be constructed in proper linear blocks. To overcome this problem neighbor designs in improper linear blocks and GN₂-designs in proper linear blocks are constructed.     

Religious residue: The impact of childhood religious socialization on the religiosity of nones in France,Germany, Great Britain,and Sweden

One of the distinguishing features of religious life in Western Europe in recent decades has been the sharp increase in the proportion of people who identify as unaffiliated with any religious tradition (religious nones). Non-affiliation entails a rejection of religious belonging, not the absence of all religious belief and practice; yet the determinants of religiosity among nones have not been fully explored. Drawing on data from the 1998–2018 ISSP surveys in four West European countries (France, Germany, Great Britain, and Sweden), I test the impact of childhood religious socialization on the religiosity of unaffiliated adults by comparing lifelong nones, who were never religiously affiliated, with disaffiliates, who were raised within a religious tradition and have since exited organized religious life. Disaffiliates are consistently more religious than lifelong nones due to religious residue from childhood, with greater residue found among those who were more religiously committed as children. Religious decline among the unaffiliated over time, combined with the increasing proportion of lifelong nones and second-generation lifelong nones who lack even an inherited, minimal religious residue, suggest that secularization will gather momentum.     

SEIR Model to address the impact of face masks amid COVID-19 pandemic

Early in the pandemic of coronavirus disease 2019 (COVID-19), face masks were used extensively by the general public in several Asian countries. The lower transmission rate of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in Asian countries compared with Western countries suggested that the wider community use of face masks has the potential to decrease transmission of SARS-CoV-2. A risk assessment model named Susceptible, Exposed, Infectious, Recovered (SEIR) model is used to quantitatively evaluate the potential impact of community face masks on SARS-CoV-2 reproduction number (R₀) and peak number of infectious persons. For a simulated population of one million, the model showed a reduction in R₀ of 49% and 50% when 60% and 80% of the population wore masks, respectively. Moreover, we present a modified model that considers the effect of mask-wearing after community vaccination. Interestingly mask-wearing still provided a considerable benefit in lowering the number of infectious individuals. The results of this research are expected to help public health officials in making prompt decisions involving resource allocation and crafting legislation.